Those satellites with their own propulsion will eventually go off and do their own thing, while initially they behave as do the non-propulsive ones.
The non-propulsive satellites simply drift along in the exact orbit they were dropped in, with the only change being a very gradual lowering of the orbit due to drag. So, what does this mean for a whole parcel of them released at almost the same time, from the same Falcon 9 second stage. Are they going to stay clumped together, and possibly in danger of running into each other?
While the smallsats are released into the same basic orbit, none of them are on precisely the same orbit, because they are released with a small but significant push in various directions over a short-ish span of time. This slight difference in speed causes the smallsats to quite rapidly spread apart, even though they are in very nearly the same orbit.
Example: Lets assume the second stage is in a perfectly circular 200x200km orbit.
If we release smallsat A prograde at 0.5m/s, and smallsat B retrograde at 0.5m/s, these two sats are still moving very much the same speed, 7788.5 and 7787.5m/s respectively.
But after one orbit of the second stage, the smallsat A will have fallen behind by 1.2 seconds and smallsat B will be ahead by 1.2 seconds.
This places smallsat A at a distance of 18.7km away from smallsat B, after just one orbit!
Strangely enough, this is both much further and reversed in orientation , compared to if these same sats were released in deep space and just drifted away.
To answer your questions in detail:
- Yes, they stay in a swarm. But the swarm spreads very quickly. After just one orbit of less than an hour and a half, they have already spread out into a line about 20km long. The sats are basically separating from each other at a brisk jogging tempo.
- As they have no means for propulsion, they can do nothing about following distance. But as (1) shows, the natural tendency of the orbit is to greatly amplify any small speed differences, causing the line to stretch out indefinitely. There is no concern for meeting any other sat in the launch.
- Most of the smallsat never slow down, other than gradual drag and eventual reentry. They rely on the deployment method and patterns to impart the initial slight velocity differences, and after that it's simple orbital mechanics that spread them apart.
The Starlinks and similar satellites with propulsion will raise or lower their orbits as they please, of course, and very rapidly depart the swarm once they do so.