1. Exhaust valve should be the one closest in proximity to exhaust manifold, intake should be closest to intake manifold- e.g. if the the intake manifold is higher than the exhaust manifold, the top valve will be the intake valve. Are the valve clearance settings going out of adjustment within a week?
2. No.
One of the experts here will advise you on possible causes and remedies.

Before running engine further, would pull dipstick and smell residual oil for presence of raw fuel. If so, immediately drain crankcase oil, replace with fresh oil, replace oil filter if so equipped. Crankcase oil diluted with raw fuel will not properly lubricate your engine - can cause catastrophic failure.
Raw fuel present in open plug port indicates carb float needle valve remaining open allowing excess fuel to flood into engine. Carb will most likely need to be removed, disassembled and thoroughly cleaned before being rebuilt.
During that process, it would be a good idea to purchase and install an inexpensive inline fuel shutoff valve(particularly if your tractor is of a gravity fuel feed design) and to replace all flexible fuel lines from the tank to the engine.
As to the valve Adjustment for that engine, There is a poster on this website by the name of Walt that is an expert in such. Hopefuly he will see this thread and respond with assistance.

Thanks guys for responding so fast. The valves are not going out of adjustment from what I set them at. If I can figure out which is which then my adjustments will stay. And since I had never done this before on anything, I saw online a couple of ways to make adjustments. Using Top, dead, center way and also when spring is fully compressed way.

What grass1950 said makes sense if I knew what is the exhaust manifold or the intake manifold. Sorry. Is there another way to figure it out?

Also, there isn't any oil filter and it is a gravity fed fuel system. So the hard starting is NOT the reason for all the gas by the spark plug port?

Sounds like NONE of your valve adjustment techniques are correct.

EXHAUST that's the burned combustion products that exit through the muffler.
INTAKE where the carburetor attaches.

Excess gas in the combustion chamber causes hard/no starting.

SMELL the oil in the crankcase!!!!!!!
Your description sounds like the carb needle/seat assembly is leaking through, allowing fuel to run through the carb, into the combustion chamber and then past the piston into the sump.
That HAS to be FIXED!!!

Walt Connor has detailed instructions on the valve adjustment procedure. Email him for a copy, giving the Model# (31C707)

If anyone has Walt's email address and could send it to me, I would appreciate it. I tried one address I found, but it did not work.

wconnor5@frontier.com

"So the hard starting is NOT the reason for all the gas by the spark plug port?"

As rcbe and Bill said: Correct. All the gas is the reason for the hard starting. I think I see your rational here and adjusting the valves is NOT going to cure the gas problem. (But, it never hurts to periodically check valve clearances especially on B&S engines.)

As has been said. Do not start the engine again until you have repaired this problem and drained and replaced the oil. Before draining and replacing the oil, unhook the fuel line from the carb. and drain the gas out of the tank. Then follow the advice on replacing the oil, replacing fuel lines, installing a shut off valve and repairing the carb.
I'm not sure if the gentlemen here would agree, but you may be bettered served in buying and installing a new carb rather than trying to repair the old one yourself.

Okay, thanks guys. I will do carb and oil service.

But I would still like to get Walt's procedures for valves...

Well first off, you miss spelled my name and do not post the correct address because "Crawlers" gleam email addresses all time from these forums which is why I do not post it.

The top valve will be the exhaust. For instructions, address below, put in proper format and remind me, model number and what you want.

Walt Conner
wconner5 at frointier dot com

Sorry Walt.

One more thing about the hard starts. When I try to start it, the engine turns a bit. I hand turn it which is pretty hard to do, try it again and it turns a little and stops. I thought this was more of a compression problem?

Sorry Walt.

One more thing about the hard starts. When I try to start it, the engine turns a bit. I hand turn it which is pretty hard to do, try it again and it turns a little and stops. I thought this was more of a compression problem?

That's the whole point of the valve adjustment-
The compression release requires the valve lash to be set properly for it to work.
There is a "bump" on the cam lobe that slightly moves a valve open at TDC to relieve compression pressure. IF the lash is just a few .001"s too much, the valve doesn't get bumped open.

That's the reason valves are adjusted with the piston 1/4"PAST TDC.

Thanks to all for their help. I drained oil because of gas smell and put in shutoff valve, rerouting fuel line. There was a solenoid on bottom of carb bowl that might not have been on correctly. Adjusted valves that were off a little and have used mower a couple of times since and have had no problems. Thanks again to all.