I did this same exact xfer a few months ago. There is a bus but after the long flight you might as well just walk: get outside, turn right and keep walking... It shouldn't take you more than 10 minutes. When you get to the T6/T7 area go back inside and take an escalator or elevator up one level to departures where you'll go through security. (LH should be able to print your UA LAX-SEA BP in FRA)

The attendant at the UA IFL didn't blink when I showed my LH F BP and onward UA BP. However, that lounge is really a dump -- after LH (presumably the FCT?) you will be disappointed. I am not sure if there are showers there. Even so based on what I remember of the bathrooms, I'm not sure I'd use showers if there are any.

The 735 is a dumpy plane, and again, after LH you're going to be grumpy regardless of which of the 8 seats you're in. If you like the bulkhead, go for it. If not, go for row 2. Same w/ window vs. aisle.

A 2025 departure is after UA's meal window, so don't expect a meal. (Even if you got one it would probably be a lousy snack box/cold meal in a plastic box, because you're likely on an ex-Shuttle plane with no ovens.) If you are hungry (hard to imagine after LH -- there are 2 full meals plus a very ample snack) pick up something in the terminal. In my experience I wasn't hungry and didn't want a shower at LAX -- just some water to ahem, rehydrate, and I wanted to be home after a long day of traveling.

Enjoy your travels -- and make sure you maximize your time at the FCT!