Quick question about bonus actions in the rules.  I'm not crystal clear about when one is allowed to possess & use bonus actions.  (clearly I'm kinda new)

Even if you're not a class/character that has any bonus action capabilities built in (rogue, etc), if you're a say, human cleric, do you have the ability to have your normal action AND cast Healing Word (1 BA is it's time cost)?  Or must you dual-class with a class that has the ability to have bonus actions?

And for two handed fighting, ANYONE can dual-wield, correct?  You just get the bonus' if you're properly trained (TWF, etc).  This has been answered elsewhere, but just confirming here, since it somewhat ties into the above.

This is a big discussion point with my DM and I.  I'm thinking that if a spell says you can BA, then you can BA regardless, and that if you have 2 daggers, you can use them, you're just not as good as a specialist.

Thanks!

Every round you have an action, a move, and a bonus action. You may not alway have something to USE it on but you always have a bonus action. 

There are spells and effects that may make you lose actions as well but in general you always have those three.

Edit: you are right in both your examples. You can use your action to attack with a dagger and use your BA to attack with another one but gain no str or dex bonus to its damage. And yes you can healing Word. 

Everyone has a free action (draw a weapon, yell, etc), bonus action (some spells, rogue cunning action etc), an action (most spells, attacks, and all sorts of things), and a reaction (something that you can do if the requirements are met, usually not on your turn - Shield spell, opportunity attack, etc).  You can use your bonus action to cast Healing Word and still use your action, but you cannot under normal circumstances cast more than 1 spell that has a spell level per turn.  You could attack and use healing word.  You could also cast a cantrip and use healing word.  Or anything with your action and cast healing word using your bonus action. You couldn't cast Cure Wounds with your action then cast Healing Word though.  Healing Word would be a pretty stupid spell if clerics didn't have a bonus action with which to cast it.

Anyone can two-weapon fight.  If you take the attack action on your turn, you can use your bonus action to make a single attack with the other weapon (you do not get additional attacks from the bonus action if you have extra attack).  This bonus attack does not add your ability modifier for damage (strength or dex usually, you still add this to your attack rolls to hit). Two weapon fighting style from the fighter or ranger lets you add your ability modifier damage to the bonus action attack.  This normally requires the weapons to have the light property but the Dual Wielder feat lets you ignore that.  

According to the Rules as Written, your DM is wrong.  DM is sorta always right but... yeah you should rectify this because it's a pretty big deal to take away a class's bonus action.

 I'm thinking that if a spell says you can BA, then you can BA regardless

Yes and no.

If a spell says it is cast as a bonus action, then it can be cast on any turn as a bonus action, provided you have not already cast another spell as an action that turn. The rules clearly state that you can only cast one non-cantrip spell per turn. So, if you cast a level 1 or higher spell as an action, then you could not cast a level 1 or higher spell as a bonus action on the same turn. You can do something like cast the Light cantrip and cast the Spiritual Weapon spell as a bonus action. But if you cast Cure Wounds as an action, then it doesn't matter if you have a bonus action still waiting, you would not be able to cast Spiritual Weapon on the same round.

You are allowed to take 1 action and 1 bonus action every time your turn comes up. However, you do not always have a valid bonus action option. For example, if you shoot a bow, then there is now TWF option, and maybe none of your spells counts as a B.A. You might then not be able to do anything. Effectively, many characters simply "pass" their B.A. on most of their turns, as there is nothing applicable to do. Just like you get up to 1 reaction per round (on someone else's go), but if nothing happens during the round that triggers a reaction, you don't get to take one.

While the above are "sort of" correct a few of the quotes on the rules concerning casting multiple spells in a turn are incorrect hen applied tocertain circumstances.

For example it is often quoted that you can not cast more than one levelled spell in a turn, while this interpretation of the rules is usually the same as what the rules actually say there are certain circumstances when it is not, for example a fighter (either Eldritch knight or multiclass) can cast 2 levelled spells using action surge.

The actual rule is
A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.

So if you cast a spell  with an casting time of a bonus action (e.g. Misty Step) you can not cast another spell on that turn except for a cantrip with a casting time of one action.  The "casting time of one action" is generally superfluous, I think you only ever have one bonus action so it would be impossible to cast cantrip with bonus action as well as misty step and I am not aware of any cantrips with a casting time of a reaction.  It does mean you can't start to cast mending that time but given that takes a minute it is rarely used whe nplayers are in initiative.

Note that the spell with a casting time of a bonus action does not need to be a levelled spell, cantrips are spells (as demonstrated in the second clause of this rule) so if you cast Shillelagh as a bonus action you can not cast a spell other than a cantrip  with your action.

Sage advice has clarified that you can cast a levelled spell as an action and a reaction during your turn, for example if you cast fireball and the enemy tries to counterspell it you can counterspell the counterspell as your reaction.

There have been some heated debates on these forums about some specific examples which I don't want to bring into a huge debate here but they mostly revolve around whether you can cast a levelled spell asa reaction if you cast a spell with your bonus action for example if you cast misty step and the enemy tries to counterspell it. I believe that the rukle above means you can not use your reaction to counterspell the counterspell but others disagree. Decide on how your table is going to interpret this.

Quote from Jegpeg >>

Sage advice has clarified that you can cast a levelled spell as an action and a reaction during your turn, for example if you cast fireball and the enemy tries to counterspell it you can counterspell the counterspell as your reaction

 Let's not turn this into a debate on that topic. Suffice it to say that the above statement is disputed.

Quote from Keeroth >>

Every round you have an action, a move, and a bonus action. You may not alway have something to USE it on but you always have a bonus action. 

 

 This is not entirely correct, just clarifying it so OP can state their case to the DM as accurately as possible. You don't technically have a bonus action unless you have a specific spell or feature that uses a bonus action (this includes TWF if you meet the prerequisite of wielding two light weapons, which anyone can do). Those things actually provide the bonus action, it's not something you have innately.