1. Yes, she can keep up with Kakashi, maybe not the entire match but for the time she needs to execute her plan she can. Also Kakashi can't run for the whole match either, he can probably outrun Tsunade for a couple of minutes and then he has to stop due to his pitiful stamina. This also alters how many strong attacks he can perform later in the battle.
2. Yes, she is reputed for her fighting skills and monster strength. (Taijutsu)
3. Her "healing techniques"..as degrading as that sounds, involve the Creation Rebirth which takes only a few seconds to activate. This provides
constant recreation of cells and organs and also provides an immense amount of chajra for the user to do whatever she wants (Yin Seal: Release).
4. If Tsunade, for some reason, let's Kakashi in close range (where she has the advantage) and also gives him the time to perform a Kamui..she can still recover almost instantly. This is assuming she stands still like an idiot and doesn't try to evade it after he performs it. This is situation is very unlikely, because all she needs is one good punch or one of her electrical waves to reach Kakashi (immediately paralyzing him). Even if this unlikely scenario takes place, she can still recover and keep battling while Kakashi is wasting chakra and stamina.
Tsunade has more chances of winning.