Accessing the chat on phone is a VIP functionality. VIP supports the development of the site. 

You must register to classes (buy all the furniture needed, then click the red button), then click a class, read the lesson and you'll see the homework requirements below, along with an empty white textbox. Type your homework in this box, making sure it fulfills all the requirements stated by the teacher, then send it and you're done. 

I do not fully understand your question. You can deposit your money in the gringotts bank and it'll give you +1% interest each day you log in. It will also prevent you from losing money because of peeves. You can access gringotts whenever you want (no level requirement, as far as I know) as long as you're not fainted. I hope this helped you. 

I believe you can always suggest your teachers to make a field trip in their lessons ? Like, the lesson before exams, the assignment is to write about the field trip, what you've seen, learnt, etc

I like this idea, however it's already been suggested here : https://feedback.worldofpotter.eu/communities/1/topics/1063-folders-for-items-in-your-chest

i like the idea, and it's already been suggested several times <3 https://feedback.worldofpotter.eu/communities/1/topics/788-away-button https://feedback.worldofpotter.eu/communities/1/topics/1178-possibility-to-go-afk-from-chat

500 galleons is enough to buy a wand and most of the 1st year books - you can always enroll in half of the classes, do some homeworks, and earn more money to enroll in the rest. 

Do you have any concrete ideas on how to do this ? New players are already welcomed by their HoH (and sometimes a House welcoming team), can read all the guides and ask questions in the chats if needed. I don't understand what you mean by "involved". 

I believe that if you take all the subjects, there is enough homework to keep you busy for quite a while : 10 homeworks time 10 subjects in 1 year means already 100 homeworks, if you take time to write a nice piece of RP for each of them, you can't really get bored. So to my mind there's no need of extra work. 

About the other activities you mentioned, I like the idea of the Gobstones Club and Frog Choir, although on most sites there are clubs involving them. I also agree with Val : how would you see it ? Playing Gobstones against the computer ? Another player ? What rules ? What cost ? What's to win ? Etc. Lastly, Dumbledore's Army is cannon therefore we can't really make an IG club with it. 

You can already earn House Points with homework (grading & submitting) and Peeves's Corner. There are even more ways of getting xp (like, logging in on a daily basis, having happy pets, chatting, roleplaying, owling, and gaining house points of course). This should be all explained on your site's guidelines - if not, you can contact your admins to suggest them these additions. Moreover, quizzes, polls and minigames aren't very much related to the Harry Potter canon - homeworks are, in comparison. Therefore I don't believe such an implement would be necessary nor doable.