Independent broker, shouldn’t cost you anything, or look yourself online and contact the lenders direct. Brokers do manage the process, though and ensure all paperwork is correct.
Make cheeky offers..why not! As has been said, the worst they can say is NO. As a first time buyer with a mortgage approved you’re essentially a cash buyer and that may make any offer you make more attractive. I offered 20k under asking price on my first house, and when they said no I walked away, 3 weeks later they phoned me and asked if I was still interested at my offer price, I was and I bought it. You just don’t know peoples circumstances and how keen they are to sell.
Don’t worry about mortgage term, you will move, you will have other houses and mortgages, just get on the ladder, you can worry about mortgage terms later.