Flooring Tile - Tiling entryway on cement

Ok, my next project is to lay tile in my entryway (3 1/2 x 11). Currently there is lenolium (spelling?) that is probably the same age as the house (20yrs).
I am going to remove this old stuff first, so, this brings the first question.

1. What is the best way to remove excess adhesive from the old floor?

Next issue I can see, since I have no subflooring, (all cement slab) and the cement is coming up in small pieces right after you step in the door. It's only the first 1/2" - 1" into the doorway. Can I pick all this debris out and fill it with something? If so, what?
Also, in the same area (corner of entryway near front door) there is a raised area of slab (3"x4") about 1/8" higher then the rest. Can I just chisel that out and apply a filler like my previous question?
Any help would be greatly appreciated.

1. Scrape off adhesive with razor scraper. Heat gun may be helpful. Verify that adhesive is not water-based by testing to see if it is water soluble with soapy water. If so, it can be removed by scrubbing. If not water-based, make sure the thin set is one that is compatible with adhesive. Not all thin sets bond with adhesive.

2. Remove loose cement. Fill with concrete patch.

3. Concrete should be flat and smooth. Raised areas can be chiseled or ground down. Use concrete patch as needed.

Thank you for the fast reply! Sounds like a plan.

Note to self:
Tile over 20+ yr old lenolium next time (sarcastic). My hands are bruised from using that scraper. What a pain in the butt! That heat gun helped a bunch, but still a slow slow process. Glad I did it myself and saved a whole bunch in labor. Just thought I'de tell ya'll that.

Ok, I'm 3/4 way through setting the tiles. It's a slow process for me since this is my first time doing it. It will probably be my last as well. My legs and back are killin me. Here a question I need to ask:

After I'm done with the entryway, I'm going to have a contractor do my kitchen.

1. What is the going rate for labor for them to install the tile? The kitchen is about 11 x 12'. Thank you!

Way to many variables to answer your question. I would suggest that you figure out exactly what you want to do, get a few quotes, get some references and make your decision from there.

Sorry for all the questions, I'm just a little ignorant when it comes to flooring. I have a couple questions now.

1. I finished laying/grouting my tile. I finished last night. There of course is a grout hazing over the tile and grout lines. When is it a good time to clean all this off after finishing? I cleaned off most of all the grout from the tile 2-3 times last night with clean water and a sponge.

2. Me in my infinete wisdom stuck two of my fats toes into the grout and didn't notice it till this morning. Is there a grout filler that I can fix this with? I don't want to buy a whole bag of grout for just this small part.

Ok, I bought some "Safe to Use" sul acid grout cleaner. The can says wait a minimum of 10 days after grouting to clean it. The issue now is, the 4 Care Penetrating Sealer I got from Home Depot for the grout says to apply when grout is fully cured (48hrs). Will it make a difference if I wait to seal after I clean the haze 10 days from now?