Got bored, found a site to do the math for me:
http://www.artificial-gravity.com/sw/SpinCalc/So if you want 1G on the inner surface of the Cylinder with 1 RPM, you would need it to be ~900 meter radius (1.8 km wide), and the surface would be moving at just over 90 meters per second.
The map of the interior would be as long as the O'Neill Cylinder, and be ~2800 meters wide, or about 93 Battlemech hexes. Shooting at target on the opposite side of the cylinder would be ~60 hexes away.
Technically you could have Mechs or ASF drifting along the interior of the cylinder, as long as they maneuver out of the way of the support pillars that attach the Cylinder to the central keel. The problem for any unit on the interior is that if it is drifting and hits a building, it will be the equivalent of that unit impacting at a speed of ~324 kilometers per hour, or a little over 200 miles per hour, or about a speed of 30 hexes per BT turn.
The other fun is firing direct-fire weapons. For every second the shot takes to reach the target, it has moved 90 meters. Hope your techs were able to rig up a calculator setup to properly lead the target, otherwise you will be rather inaccurate. And since you will be punching holes in the metal that is keeping the air inside the O'Neill Cylinder, the locals will likely consider you to be genocidal. Best bet might be using PPCs and laser weapons for direct-fire, along with guided munitions (Artemis, Streak, TAG, etc).
Best bet - station a few ASF outside the Cylinder and tell the inhabitants that you need to come on board to turn off those radars to ensure they are not going to be used (or at least put monitors to make sure they do not go above a certain threshold). If they refuse to let you land, the ASF can do small and careful shots on the radars. If the O'Neill Cylinder opens fire, it is a military structure that must be taken out.
Tell the locals to turn off the tracking radars for a certain period of time (i.e. during your planetary invasion), or only allow them in certain directions (i.e. away from the planet). Also require that the locals share their radar data with your ships so your ships can help with destroying debris before it gets close to the station.