Reputable enough firm. Fidelity has good tools. Doesn't cost too much. It's probably best to avoid having a long chat with the Fidelity representative though. Some of them like to pressure customers into investing additional amount into a Fidelity account, etc. If you must have a long consultation with them, it's best to do your own homework and have a good idea of what you want to do, so you won't be steered into something that they want you to buy.
Yes.
I use Fidelity and I would recommend them.
I want to buy some stocks, mutual funds and open up an IRA account.