A satellite orbit can be in several shapes, but I assume we here restrict ourselves to talk about satellites in circular orbits.
You are correct, that if you compare a satellite in one such circular orbit with another in a lower circular orbit, then the lower satellite will have the largest magnitude of centripetal force of the two. However, the equation you quoted, which relates force, mass, (tangential) speed and radius of a mass in steady circular motion, does not directly reveal this since you do not, without any additional knowledge, know how the speed of the two satellites varies with orbital radius. But since you know that gravity is the only force around to keep the satellites in their circular orbit, you can equate the centripetal force with the force of gravity on the two satellites and so, if you know how the force of gravity varies with radius you also know how the centripetal force varies. (hint: look for an equation describing Newtons law of gravity).
For the remaining measures mentioned (period, tangential and angular speed) there are many ways to go about explaining what happens. The easiest way if you have access to the equations relating these to one another and with orbital radius is to show how each measure varies when orbital radius is decreased. Try look in your textbook for equations that include such relations and see if that will bring you forward.
Regarding the difference between angular and tangential speed of a circular motion, then the angular speed is how much "angle" as seen from the center of the motion the object travels per time, that is, if the satellite in this case travels a full circle in 90 minutes its angular speed is 360 degree / 90 minute or 4 deg/min. You can of course convert this to other units like for instance radians per second or similar.
The tangential speed of an object relative to some reference point is simply the speed in the direction that is perpendicular to the line between the object and the reference point. If the object is in circular motion then its velocity vector is tangential to the circle (hence the name) and thus is always perpendicular to the radius so in this case tangential speed is simply the speed of the object at any given instance. If the circular motion is also steady, then the tangential (and angular) speed is constant and you can calculate it has how long an arc it travels per time. For instance, using round numbers, if a satellite is moving around the Earth every 90 minutes or 1,5 hour and travels 42 thousand kilometers in one such orbit (corresponding to the orbit being around 300 km above ground), the speed is 42000 km/1,5 h or around 28000 km/h og 7800 m/s.
