Actually, you can skimcoat yourself - it is time consuming but not hard. (I had no DIY experience!) My entire house had this heavy knockdown texture on the walls. You get a box of Sheetrock drywall joint compound, take some out and mix some water into it to get it easier to spread, and then smooth it on with a big drywall "knife". Let it dry, sand it down, and then repeat. I used a vacuum attachment for a shop vac when doing the sanding and it really minimized the dust. I worked on it every evening and saved a ton of money. If you want, I can post links to the materials I used. I think my actual materials probably cost less than $100. (PS I am a woman "of a certain age" so if I can do this, anyone can!) You may decide that you can do the bulk of the work and then have a painter come in and do the "finish" coat, which would still save quite a bit of money. The main thing is that if you hire someone to do the skim coating, it takes several trips because each coat has to dry and then be sanded, and it will probably take 3 coats (depending on the original texture.)

If you can fill small dents by dabbing in the compound, then yes you can do this - compound sticks fine to paint. I have taped new walls to existing painted walls many times. If you want to fix the joints and feather them out, then your husband is correct - you need a smooth level surface. Even a single screw head sticking up 1/64" will mess up a finishing job since the taping knife hits that bump as you are finishing. That is why I always scrape my surface level between coats - any little chunk or bump raises havoc. For tips on finishing drywall, see the site below. Here is a link that might be useful: Taping and Finishing Drywall

Best would be to repair the drywall, but if it is a half inch stip vertically and you are in a corner, then the tile will only be backing that gap the one half inch minus the thickness of the tile. You are talking about 1/8 to 1/4 inch. For 1/2 inch mosaics, that may still be significant, but it you are doing 4x4, 3x6 or other common size larger tiles, I wouldn't be too concerned about it. That little strip isn't going to bear the load of the tile or have weight on it (like a floor would) to make it crack. The mud will be solid enough to keep the tile from moving and that might be the most important thing for such a small area.

I to have tried my hand at tapeing and texturing a few times over the years,what a mess!. Here's how I handled the last few projects,including a couple of room additions, a house that had fire damage and a few patches like yours. Around here builders don't keep sheet rockers on payroll so 1 and two man subs picking up day labor help, operating out of 1 truck pulling a trailer is common. I drive through new additions looking for a drywaller at one of the new houses and ask him to come by to bid my job. I have hired them for various stages from hanging to tape and texture and always been well pleased. If you are bent on diy all the way,buy a case of Bud Lite and give ne a call to come show you how. After it's screwed up beound hope we can go look for a pro to straighten it out.