Sealing MDF so It Doesn't Absorb Moisture

You do not actually need to seal the MDF so it does not absorb moisture, any more than studwork in walls, the interior components of cabinetry or the framework in covered chairs need to be sealed. Regardless of whether it's solid wood or a type of manmade board the material can be left to absorb and release moisture naturally with any changes in humidity. In any case the whole concept of "sealing" is commonly misunderstood, with only a few exceptions the coatings applied to wood do not truly seal the surface off from water vapour*. However, it looks like the natural colour of the MDF wo not suit the completed panels so I think you need to paint them. Normally when someone is looking to paint MDF the recommendations are about how to get the surface looking good since it will be on show (e.g. filling/sealing the edges, then primer and finally paint, with quite a bit of sanding thrown in there). But here it seems like you really only need to change the colour so you could go straight to paint. Matt black seems like it would be the ideal colour.*This is why even a fully varnished tabletop will still expand and contract through the seasons as humidity goes up and down.

1. How to attach a rim joist on Free Standing Deck an inch away from the house?

If you are building a "free standing" deck, then why are you wanting to attach it to the house? The proper way to build a deck that is attached to any house is to start at the house. Sounds like you went backwards on this project. You can see why because you have no room to work, now. First, you would install a ledger board to the house and proceed to build the rest of the deck off that ledger board. The board that is between the house and the deck is not called a "rim joist". At this point, you will need to use "Teeko" clips or metal fasteners to connect back to the house and a thicker ledger board to take up the last 1" of space. After fastening the ledger board to the deck with metal fasteners, you can proceed to fasten the same board to the house with minimum 1/2" diameter lag bolts/flat washers. Make sure they are long enough and that they go into solid wood (i.e. - floor joist is best or rim joist). Seal the top edge of the new ledger board to the house as to eliminate water intrusion.

2. Exterior Sheathing with highest r-value?

Exterior sheathing, such as T-111 or OSB, have little to no R-value. Solid wood has a R value of 1 per one inch of density. Where wood shines as an energy efficient product is heat retention. For example, a typical log home of 8 inch diameter logs only has a R- value of 8. However, the physical characteristics of the wood allows it to absorb and retain interior heat, creating a radiant heat effect.

3. What do Americans call the wooden battens fixed across the end grain of solid wood table tops and drawing boards?

As Dennis points out, a Google search for "breadboard end" gets lots of hits, e.g. Breadboard Ends . Don't goof up like I did by gluing them down completely (one of my panel boards split open).What do Americans call the wooden battens fixed across the end grain of solid wood table tops and drawing boards?.

4. What is the difference in re finishing or refacing the kitchen cabinets which is less expensive?

Trying to refinish a door is more trouble then it's worth and still not always possible. Think of all the grooves and nooks and crannies that you will have to sand with your finger tips ground into the sand paper. Also keep in mind many doors might just be a veneer rather then solid wood. If you try to sand veneer a sander would go through it in a blink of an eye right through to the particle board core. Replacing is an ok idea. We used to buy ours from Decorative Specialties out of California. You can order each door and drawer face by it's wood species and to the exact size. They have several hundred door and drawer styles to choose from. They run from $25 each for a little door such as above your fridge or micro to maybe $125 for pantry doors. Drawer faces around $20 each. The average being around $50 each for oak, slightly more for maple and much more for cherry. Keep in mind if you buy new doors you will have to drill the 32mm holes with a forstener bit and a very strong drill. Can you do this? The 32mm holes are for any standard concealed hinge. You would not have to drill if you do a wrap hinge but they are so fugly and outdated you will defeat the purpose. With wrap hinges you will have limited choices of door styles because the door edge has to match and except the wrap hinge. And do as you say...do not paint cabinets. They will look horrible.