1.) Does Aegean still award a 1,000 miles sign-up bonus?
Yes. Clearly written on the homepage.
MILES+BONUS More options, more miles.
Join now, earn 1,000 welcome miles and discover numerous reasons to be a Miles+Bonus member

rest, details here (Chapter 9): https://en.aegeanair.com/conditions-...nd-conditions/

2.) If after booking a flight I remove them from the account, do all the remaining miles stay in my Together account? (logically I think they would)
There are two types of miles, tier miles (to earn silver/gold tier) and award miles (to redeem for stuff).
The tier miles always remain with the original owner (and are not pooled), while the award miles remain with the Together account owner.

3.) Would inviting them and then removing them restrict me to inviting only 1 more friend in the future, or 3?
Yes, you can only remove people after a year, meaning at most 5 new members (excluding you, the 6th member) within 12 months.
Details in the URL above.
The particular accounts you added then removed can not participate in any other together account for 6 months from date of removal from previous together account.
Also, such accounts added to a Together account cannot be removed in less than 12 months from the join date.
A Together account can consist of 2 to 6 members.

Together accounts aren't there to be misused for pooling of miles, and yours could be frozen if suspicious mileage pooling is suspected.
the members dont need to be family, but frequent adding and removal of accounts would constitute suspicious activity.
I suggest you do it only if you are ok with having those two accounts lying dormant in your together account for a year.