What I mean is, does the target’s velocity value directly affect the seeker, or does the velocity value get calculated into a Doppler signal strength, and then that signal strength affects the seeker?
Kind of, yes. In ground clutter, the faster a target is moving towards or away from the missile, the easier it is to see it.
Not really sure what you are trying to ask here. The pulse doppler filter is not meant to increase or change the signal strength, that stays the same. It is just to make targets stand out on top of ground clutter by detecting a change in frequency of a returning radar wave to see if whatever the radar is pointing at is moving at a different speed to the ground.
As far as I’m aware, radars cannot actually use the doppler effect to give the pilot a readout of the target’s speed because the doppler effect only accounts for the velocity relative to you, so if they are flying at an angle to you, that speed would be inaccurate. Instead, what it needs to do is track how much the target moves in each axis over a certain amount of time and then use that to compute the speed. I can go into more detail about this if you like.