As for the rest:
"Shares transferable to any type of future share issued at a 1:1 level?"
That's pretty standard: Seed Preferred is probably the most flexible form of share you're going to issue. 1:1 to common is usually what they want, so they can cash in on an IPO. Transferring Seed Preferred to Series A preferred would be weird, since the seed investors are usually at the top of the pecking order in terms of payout.
"In the event that future shares are issued at a lower price, additional shares will be issued at no cost to investors so their average cost per share is the same as the current round."
This is known as anti-dilution protection. It's pretty common. Ask them whether they're doing full-ratchet, broad-based weighted average (what this sounds like), or narrow-based weighted average. Full-ratchet anti-dilution terms are pretty draconian, weighted average less so.
"Investing body may require that company engage 'investing body' management services."
This is too vague. Are they requiring that you do business with their management firm in exchange for the investment? That's kind of sketchy.
"Permanent put option (at specified terms)."
Depends on the terms. Treat it as part of their equity.