If the current slab is at least 3000 PSI concrete you will never generate that force on that deck even with dynamic forces. If your posts are 6X6 then the weight that slab should be able to bear on one post is about 81,000 pounds dead weight. Of course you will only have about 15,000 pounds maximum distributed over 8 posts. I wouldn't tie the deck to the house though if you are in a freeze thaw climate. The slab will raise and lower during freeze thaws. This might damage the siding or facade. If the concrete has large voids underneath it then the load it can carry will greatly decrease, and may not be able to hold the deck without cracking. If there is wiremesh in the slab or rebar the flexural strength will be enough to span a small void. Either way the crack wont open up if mesh is properly installed.

I believe (based on my own experience, not expertise) that it's just going to disappear soon enough. However, I just bought myself a steam cleaner which arrived today, and I have been happily cleaning just about anything I can find with it!! And I think I would try the steam cleaner on your concrete stains!

What product and color did you use? Anything can be accomplished if you have the money. You could sandblast your drive and restain, for example.

Maybe a degreaser for concrete garage floors or driveway would help. Also, might try rubbing cornstarch or other dry powder into it to help absorb/wick up some of the oil. Repeat applications would be needed. After removing the oil spot I would put a good concrete sealer on the counter to prevent future stains from food/cooking. Enough coats of sealer until water will bead up on it instead of being absorbed.