Familiars retain the benefits of being a familiar even when true polymorphed
Nothing about true polymorph cancels the effects of the find familiar spell. The benefits of find familiar such as telepathy and the ability to deliver touch spells are not statistics of the familiar (they aren't listed in their statblock) and thus aren't replaced by true polymorph.
Remember the general policy for two spells interacting as stated by Jeremy Crawford:
Spell A doesn't cancel spell B unless the text of spell A says it does.
Transforming into a homunculus will give you telepathy while on the same plane
The statblock for the homunculus says:
Telepathic Bond. While the homunculus is on the same plane of existence as its master, it can magically convey what it senses to its master, and the two can communicate telepathically.
While not canceling the effects of find familiar, in this case true polymorph would add to the familiar's abilities because it is changing the underlying creature's natural abilities. This is not changing anything about the find familiar spell's effects though only adding an ability to the familiar itself.
You cannot gain infinite range for casting spells through your familiar
As stated in the first section, nothing about true polymorph cancels the effects of the find familiar spell. Thus, you can still cast spells through your homunculus familiar because find familiar says:
Finally, when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell. Your familiar must be within 100 feet of you, and it must use its reaction to deliver the spell when you cast it.
Note that the range, 100 feet, has nothing to do with telepathy. It is a separate range listed in a separate part of the spell description. Thus, increasing the range at which you can communicate with the familiar telepathically will do nothing to increase the range at which they can deliver spells. Nothing about true polymorph or the statblock for a humunculus specifically states that they increase the range for familiars to deliver touch spells, so they do not.
Also, note that mage hand is not a touch spell so it cannot be delivered through a familiar regardless. (thanks @v2blast)