It’s maybe okay for the first layer to be flattened a bit - that’s good for sticking it down - it’s hard to know if it is too much without seeing.
You are correct that one cause could be that the the nozzle isn’t getting clean. (If it isn’t clean it can push down harder on the washers and then it will “think” the bed is lower than it really is. If you watch the washer corners during bed leveling, then you should not see the washers move when the nozzle taps them.)
Of course you can also experiment with some slicer settings. You could try to change “initial layer thickness” and see if it helps - I think the default is to have the first layer thicker than the rest. The tooltip for this setting in cura says having a thicker first layer will help it to stick more, but I usually change it so it matches other layers and that still sticks fine for me. (I’m sure there are other settings to look at also.)
For stringing you might try to lower the temperature slightly (a few degrees)… Retraction settings might be more complicated, but just some ideas if you want to play around and see the effects.
The following may not directly address the issues you mentioned, but another thing to try early on is to calibrate e-steps/mm. Basically you would measure how much filament is extruded when you manually request to extrude a set amount (usually try 100mm.) If it is extruding too much, then you can turn down the esteps/mm by appropriate amount with some console commands from cura (or on the LCD if you have it.) Repeat until it extrudes the amount that is requested and save the setting. There are detailed step by step elsewhere if you search for calibrating esteps. Have fun