Using Pact of the Blade against an opponent

I want to keep this simple so ignoring anything that allows for additional STR/DEX/CHA damage.

1st -  If my bonded weapon has the push property.   Am I able to push my opponent as if I have the Push weapon mastery?

2nd - I have Thirsting Blade & Eldritch Smite and True Strike spell.   My weapon hits twice.  My damage for the 1st hit is weapon damage dice, true strike (1D6) & Eldritch Smite dice.   My 2nd hit damages with the weapon dice and true strike?

2. You can't attack twice with True Strike in the same turn unless you somehow have a second action. Thirsting Blade gives you a second attack when you take the Attack action; casting a spell like True Strike requires that you take the Magic action.

I am trying to understand this and not sure if I do.   I can have two attacks with my weapon, but only use true strike once as the magic action is not at the same time as when I attack?

You can take one action on your turn. There are several different types of action.

One of these is the Attack action, which normally involves making one attack. Your Thirsting Blade invocation gives you the extra ability to make two attacks instead of one when you take the Attack action, as long as you’re using your Pact weapon.

Another type of action is the Magic action, which is used to cast spells. True Strike is a spell, so to cast it you take the Magic action. It’s a spell that involves making an attack with a weapon, but you’re still taking the Magic action, not the Attack action, so Thirsting Blade doesn’t apply.