-Detraining to strength training begins to happen after about 3-4 weeks of ceasing strength training. However, the fall-off is gradual, and it’s likely that some of the workouts on the bike, especially explosive workouts like sprints, work as maintenance. My unscientific coach’s opinion is that if explosive (sprint) power is maintained, we’re doing things right.
Strength is also specific, so when you cease doing an activity like a squat, you’ll get worse at it. How much that matters to a cyclist is another question.
Finally, when you re-start strength training, your ‘strength’ will increase very rapidly back to previous levels, which is a sign that at some level, some of the adaptations from previous strength training hung around, whereas other adaptations come and go quickly.
The same thing exists with endurance training (just over a shorter timeline), that’s why after a week off you’ll feel pretty terrible on the bike, but after 7-10 days training you might be basically back to normal.
-Above answer probably answered the strength portion of your second question: yes, especially some specific aspects of strength, but hopefully not the things that make you faster on the bike.
Muscle mass may or may not drop over the course of the season: this is due to a mix of training habits, diet, and to an extent, genetics (see Andre Greipel’s legs vs Nairo Quintana’s legs even after a 3-week tour).
Also, a lot of athletes mistakenly think muscle mass drops: during weight training you’re often walking around with a ‘pump,’ not to mention full glycogen stores, which makes muscles look bigger. When you lose this pump, and have more days where muscle glycogen stores are depleted, you can mistakenly think that a loss of muscle mass has occurred.
-That’s a pretty ‘it depends’ question. If your last A race of the season is in early August, but you decide to continue racing until early October, then yes, you may notice you’re off-form and running on fumes by the end of the year.
Also, if you peak for a hilly road race or a TT in May, and then you peak again for a block of crit racing in August or 'cross season in the fall, then your FTP may be slightly lower for your second peak, just because of the training necessary to be sharp for criterium racing or cyclocross.
But in general, if your FTP just steadily drops throughout the season, you did something wrong.
-You may start from zero in the adaptation phase (nice to avoid the brutal soreness that comes from starting too hard in the gym), but you’ll advance very quickly to your previous strength level.