Can't do anything about the times, but.
Baggy trunks - easily fixed. Buy a couple pair of speedos, and you're good to go.
Real swimmers only shave for big meets, not when in heavy training
There are lots of fast guys who never wear a cap in training, they're too damn hot.
As for counting laps, easy. If you're doing a long continuous swim, break it down to a set of repeats with zero rest. eg an 800 straight becomes 4x200 without a break. Then just count the 200 and also keep track of how many you've done.
For keeping track of repeats, try to avoid doing sets that go on the same interval. eg 20 x 100 on 1:30, you'll always be leaving on the 60 or the 30. Better is to do 20 x 100 on 1:35 then you're leaving on the 60, 35, 10, 45, 20, ... Much easier to figure out where you are in the set by doing a little math.
Swimming Workout of the Day: Favourite Swim Sets: 2020 National Masters Champion - M50-54 - 50m Butterfly