I'll see if I can answer some of your questions...

"(1) What are the SMALLEST size cans out there? And are smaller cans more difficult to install than the bigger ones?
Generally for recessed down lighting, a 4" can is the smallest one should go."
Installation of the can are not really an issue, it is more of a lamp replacement issue. Harder to replace a lamp inside a 4" can than a 6" can, less room to maneuver your fingers!

"(2) Are 4" (or smaller) cans a fire hazard while 5" (and larger) cans are not????"
It depends on the manufacturer's recommendations, whether a fixture is IC rated or not. Common speak, if the enclosure or assembly of the fixture is fire rated or not. Even if a fixture is NOT fire rated, an inspector will usually allow two layers of 5/8" drywall, in a box shape, around the fixture. This adds additional burn time before the fire reaches the attic.

"(3) Is it true that recessed light dimmers will *not* work with energy efficient lights?"
I am assuming you are talking about the CFLs. The first generation of CFLs were NOT manufactured to work with dimmers, yet people used them this way, thus cutting the life of the lamps down. Newer CFLs are labeled for dimming purposes.

"(4) What lights / voltage is recommended for recessed lighting?"
110V-120V is fine. Low voltage is generally better for track lighting.

"(5) Is it "harder" to install a fan with a shorter "rod" or "flushmount" fans (for a low / shorter ceiling) than one with a longer "rod"?????"
Just the same, unless the installer attached the blades BEFORE lifting the assembly up. If your electrician is having a hard time installing a fan, go to the next one. Also, a ceiling fan rated junction box will need to be installed. These boxes are rated to hold weight of 50 or more pounds.

"(6) How "difficult" is it to install a dimmer for the lights and program a remote control for the fans?"
Two part question.
1.)To replace an existing single pole switch(common in bedrooms, baths) with a dimmer, simply remove existing and replace with new dimmer. To install a NEW dimmer switch next to an existing switch requires adding wire and fishing it thru the wall into the ceiling and to the fixture.
2.)Remote control for the fan is wired in between the incoming wire(existing wire in the ceiling) and the fan. VERY easy to do. It is basically a black box with a remote wire, power(black), neutral(white) and ground(bare copper or green) wire for incoming, and a power(black), neutral(white), ground(bare copper or green) and light(blue) wire for the fan. The box sits in the junction box of the fan.

1) What are the SMALLEST size cans out there? And are smaller cans more difficult to install than the bigger ones?
4" cans are better suited for accent lighting. Geneal lighting is better done with 5" or 6" cans. Fire hazard?? no difference. Just make sure to use IC cans with ceiing insulation. All are available in 120 Volt and 12 Volt. Use good deep baffles or reflectors for good quality, low glare lighting.

2. Just make sure that cfl's are dimmable and use a good quality dimmer.

3 Installing a fan with either rod should have the same difficulty. Don't let them install the blades first. this can cause warping of the blade irons and result in shaking. This is a common technique that electricians use to save time.

4. If you have an exisitng switch for the lights, just change to a dimmer--easy. Wall fan controls can usually be added easily if there is an existing switch. IF not, put the control in a seperate wall box to cut down on the heat that build up in the wall box. The control will last longer. Or use a hand held remote for the fan.

5. Cost can vary by your selections. Decide what products you want to use, then ask the electricians to give you a price to install YOUR selections. Some will give you a price by the job and some will geive you a cost per hour. If by the hour be sure to get a realistic estmate of the time involved and make sure he knows of any extenuating circumstances you may have. Having the products selected before and having the information for him to see will help him with his time estimate. Don't be bullied into using only the products that he may like, sometimes there are other motives behind this. He is being hired to install your products, it should not matter to him what you buy as long as you buy the correct items for the application. A good showroom in your area can help you with this. Make sure that you have everything on hand before he shows up to install them. Have a clear understanding of just what his price includes. If he won't come to you job site to give you an estimate, call someone else. He can't know what is involved over the phone. Make your tentative selections, have the information available to show him and confer on any other items you may need to purchase, then order or purchase the materials. Make an appointment with him to install the items after you have everything you need. This way, there are no excuses for him having to come back and charge you extra......because you didnt have everything he needed. This is when purchasng your materials from a good showroom with knowledgeable salespeople can really save you money in the long run.