will i kill my lawnmower if i add the wrong kind of oil?

Checking for tune it! oils, and I find 10W30, 15W40 and 80W90 grades.
The first one is just what you need, the second is a little to thick but correct, especialy under warmer climate, but the last one is MUCH to thick for your use.

Assuming you did not add that oil to the gas, lot of smoke, especialy if it's blue, mean that the pistons segments are deffecive or that you got a brocken gasket.
Oil spilling from a side hole strongly hint a bad/brocken gasket.

My guess is that that engine realy need a qualified mechanic who"ll take it appart, clean it thouroughly, replace any deffective gaskets and re-assemble it correctly.

Electro
May 2016