bitcoin wallet is just a software like any other software so adding these features is not hard or unheard of but some of them have no use so nobody wants it like twitter feed! why would anyone want to see twitter feeds on his bitcoin wallet?!
but price is useful and it is already implemented in Electrum (i don't use other wallets to know more) it is in the plug ins window.
to my knowledge there is none (but i may be wrong) because it is a string (json or other formats) that you receive and work on that so it can not be in any other format or like be malicious! it doesn't make sense to me.
as for your IP, yes the site sees your IP based on your code you are just asking the site "give me price" nothing else so the site sees this "IP address XX.XX.XX.XX is asking for price through an API call" that is all. (unless your wallet is shady and sends more information intentionally ) in other words there is no way an API call to get price for example can reveal your bitcoin addresses.
my knowledge about this matter is limited but there is a difference between sending a message through channels that satoshi had in mind (like alert keys) and a twitter (third party and potentially insecure) channels.
the following are Electrum plug-ins and to be honest i have no idea what half of them do and i don't care either because i don't find any of it useful for me
is there any particular feature other than twitter feeds and price you have in mind?