G'day Cirillo,
A little piston movement isn't that unusual in a Briggs. As far as compression goes, the 'Easy-Spin' engines have an exhaust cam that holds the valve slightly open just before TDC on the compression stroke, so there isn't much 'felt compression' when pulling the engine over with the starter. Briggs say that loss of compression at operating revs is negligible.
This is the compression check procedure from the Briggs Service Manual:
Spin the flywheel counterclockwise (flywheel side)
against the compression stroke. A sharp rebound
indicates satisfactory compression. Slight or no
rebound indicates poor compression.
Running heavier oil is not recommended; just use an SAE30 monograde, and see if it uses any.
Unless the cowling has been replaced, those numbers should be there, but can be obscured by paint if it's had a repaint.
On that particular engine, they would be on the main cowling. Either on top near the spark plug, or on the side adjacent to the carby. The stampings may be just the number string; some models had the 'Model Type Code' part on a decal.
