For your first question, the most simple answer is Km tells you binding affinity. In general, if you have a very high Km value, the binding affinity is small. A low Km means binding is strong. Don't memorize here... realize if Km is small, that means that it requires less substrate to get the enzyme to do it's thing. The enzyme loves it, and it binds tightly. A high Km value means you need a lot of substrate to get the enzyme to act on it. Enzyme feels kinda meh about the substrate in this case.
Vmax is simply the rate at which enzyme's do their thing. This is concentration dependent. The more enzymes you have, the higher the Vmax because even more enzyme's are doing their thing.
Now, knowing this information we can apply it to certain inhibitors. Noncompetitive inhibitors bind else where on the enzyme. The active site becomes pretty messed up due to this because the binding of the inhibitor else where on the enzyme changed the enzyme's conformation. Remember the active site and substrate are "lock and key", if you beat the hell out of the lock, the key won't properly fit anymore. If the key doesn't properly fit anymore, the lock necessarily will not unlock at the turn of the key either. Ie. the rate at which the enzyme does its thing (Vmax) will go down.
Now you have a competitive inhibitor. Remember Km is the value which tells us the affinity for the enzyme to the substrate. In competitive inhibition there is something other than the original substrate binding to the enzymes' active site. So, before it was just the enzyme and substrate, it could easily take it up and bind it. Now you have the substrate + the inhibitor. The enzyme is less likely to pick up the actual substrate because now it can bind the inhibitor too, i.e affinity for the substrate goes down... which means Km value goes up (due to reasons explained in first paragraph).
Hope this helps. Sorry if I made a mistake... if something seems off lemme know, no time to proof read lol
