The second question is easy: RealtorsÂ® may suggest a lending institution to assist their customers and clients, but I can't think of a circumstance that obligates you to use "their" lender.
Many times we recommend a lender because they can deal with the situation of the buyer or we have dealt with the person before and know they're good at what they do.
If you have a lender that you're confident can help you, you should stick with what you want, although a second opinion won't hurt.
If you don't have a lender, at least start with the suggested person and try at least one more lender, to be sure.
The first question is a little more complex.
Think about it as a food server at a restaurant. RealtorsÂ® work solely for commission, similar to waiters. If you talk to a waiter, discuss food items and then order food from one waiter, you wouldn't tip a different waiter. That would be ethically unacceptable.
But if your waiter doesn't meet your needs in some way, you need to ask for help from the manager (and maybe get a different waiter). The bad waiter will eventually quit his job if he doesn't change, simply because he won't earn enough.
Similarly, RealtorsÂ® leave the business when they can't please customers and earn income.
Are you legally bound to a particular RealtorÂ®? No, unless you sign a representation agreement (for them to be your server).