Sure, but being within one's rights doesn't mean one is acting rightly. Then, Twitter was not acting rightly. So far, it is acting rightly now.
Sure, and if he starts being biased in favor of one side or the other, then I will exercise my right to object to what he's doing.
Here is why Twitter banned Trump
https://blog.twitter.com/en_us/topics/company/2020/suspension
Twitter is making leaps of logic when it says that Trump announcing that he will not attend the inauguration was being received by some as confirmation that Trunp thinks the election was illegitimate. Twitter then says Trump is doing something wrong by saying his 75,000,000 voters will have a giant voice into the future and will not be disrespected, etc.
That, says Twitter, is incitement to violence.
If you cannot see how bullshit that is, then you aren't thinking logically.
It doesn't matter that some of Trump's supporters went bananas and started chanting "hang mike pence." First of all, there is literally nothing wrong with chanting "hang" some politician or other. it's been done for hundreds of years. Democrats brought guillotines to anti-Trump rallies and pretended to behead him. They burned him in effigy. Madonna "dreamed of blowing up the white house." Democrats called for "unrest in the streets" and comment after comment for years which "incited" their supporters to conduct protests where violent acts occurrd.