I am trying to infuse the gem on my Infiltrator armor with enhanced weapon.  I even created a homebrew item (hand crossbow).  However, I cannot use the infusion on it.  What am I doing wrong?

Text of the launcher - Lightning Launcher. A gemlike node appears on one of your armored fists or on the chest (your choice). It counts as a simple ranged weapon, with a normal range of 90 feet and a long range of 300 feet, and it deals 1d6 lightning damage on a hit. Once on each of your turns when you hit a creature with it, you can deal an extra 1d6 lightning damage to that target.

As written is NOT a magical weapon.  Therefore I should be able to infuse it.

We can't homebrew non-magic items at this time, so unfortunately homebrew weapons don't count as targets for infusions because they are magical.

So then why can't I chose the Armor's Lightning Launcher itself? It isby default a non magical weapon.

The Lightning Launcher is a special Action that DDB adds to the sheet. Infusions can only apply to items in inventory.

You'd basically need to just add a weapon to inventory and apply the infusion to it, and note for yourself that it's supposed to do lightning damage instead.