3) What do you think is an appropriate cost for posting a thread vs a comment?
Very small initially would be best....
5) What features do you think could be added to further incentivize use of the site?
I think you should use the post fees to encourage community determined quality (i.e. try to foster the type of people you want there at the start, then structure a fee schedule so that positive and negative feedback loops drive behaviour)
Some possibilities:
1. Consider making the fees a bond; people recieve some or all of their money back after some condition/s has been met (you can do this pragrammatically using bitcoin script IIRC)
a. Users could maybe receive back bonded payments to the forum according to how much they receive in tips from others
b. An "Account opening bond" could be set high to disincentive ban evasion, which is lost when a user is banned
c. Set a minimum "Account open" bond, but make it possible, and publicly provable, to submit a bond higher than the minimum
2. Tier payments based on forum status
3. Make a status level beyond which high status users receive some proportion of the fees paid by low status users. Persistent bad actors would end up paying good actors so that they can behave badly
4. Make it reasonably easy to understand the system
Above all, moderators need to be knowledgable & fair. People won't join if they don't trust the management.
6) Which name do you prefer? lnchat.org or lightningchat.org? Both domains have been already bought by us
Neither, those names are appropriate for this custom forum software you are developing, not for an instance of a site using that tech.
I would suggest adding to your mission statement, as Lightning tech itself will eventually become too niche and esoteric as it becomes increasingly extensive, and as that enxtense is abstracted away from lightning users. Doing something that sets the pace against other bitcoin forums would have more longevity and wider appeal.