The last person to ask those questions is a Realtor.
1. The main benefit of a Realtor is access to listings before they hit the MLS (that is how I bought my home) and access to lazy buyers who are not looking at the online listings. And Realtors tend to steer their clients away from Redfin and sale by owner homes because that is the racket they run. Realtors also have proprietary sale contract forms that you will get to use and do help with the whole EMK, inspection, escrow and closing routine. Otherwise, it is pretty hit or miss with Realtors. A few really know their market and can tell you everything from schools to crime to noise and so on for every house you look at. They should also know the market and help you with the sale price negotiations and any concessions you may need to make after the inspection. Most anyone can handle all of this on their own, but it is a chore and there are pitfalls in trying to do it without anyone helping you.
2. If you go online and just go with the lowest rate you can find (taking into account the fees and points), you will end up with a scummy mortgage broker who will try to bait and switch you by claiming that your loan can't make it through underwriting. My dad has 800+ credit and a solid investment portfolio. When he financed a condo in FL with an online broker, they told him that they would have to redo the deal with a higher interest rate and fees because of problems in underwriting. He had to get his lawyer friend involved to get the loan closed. They almost didn't get to closing. Get recommendations from friends on local mortgage brokers and shop rates at a few. Having a smooth loan process and closing is worth paying a few extra bucks a month on your mortgage.
Interest rates are too high to make it worth it to take some cash out unless you need it for renovations/repairs to the home. And the prices are still a bit frothy and appraisals are stingy. You will not want to over extend and be upside down if the market hits the fan. Also, you will need to reinvest what you get for selling your current house into your new house to avoid a tax liability if you sell your current house for more than you paid for it.
3. ARMs are for idiots. Even with rates being higher than they have for a while, it is better to go fixed and then refi if rates drop. If you have an ARM and the rates keep going up during the teaser rate period, you are screwed and could be in big trouble if the market drops and you cannot refi.