My $0.02....
Looking at some various melomel recipes here in the mead recipe database, you're looking pretty good for your fruit addition based on what others have done.
Having never done fresh fruit, I can't answer #2 with direct authority, but my guess is that would SUCK and I probably wouldn't do it. Freeze and thaw, slight crush, that's what I would do.
Mead is whatever you want it to be. If you want to go with a purely traditional mead, then no additives should be added. However, if you want something drinkable and not looking for awards for the best traditional no-additive mead, then I would just use the nutrients as needed for a better overall fermentation. Without nutrients and such the yeast could stress and produce a long and slow ferment with potential off-flavors and smells. You just have to ask what you're doing this for. If it's your first time making mead and you're doing this to drink and share, then why would you care if it has nutrient to help the ferment or not?
Fruit in primary vs secondary is oft debated. Primary fruit additions allow the yeast to eat the sugars in the fruit and produce a less pronounced fruit flavor, with a little more complexity to the product...but it might not taste "like raspberries." If you fruit secondary, the yeast should be done with most (if not all) fermentation and the juice you'll be adding will be for a more pure raspberry flavor. Some do primary only, some secondary only, some do a little of each. It really depends on what you've done before that you know you've liked and do it again. If this is your first melomel, I'd recommend secondary, then do some trial batches with stuff in primary, or a mix of both as you get into it.
Mead can take a year, or two, or it can be 6-10 months. Depends on the fermentation and how well it goes, how much residual sweetness you want in it, how much alcohol it contains. Dryer and higher abv meads take longer to age that bite out. Sweetness hides a LOT and is drinkable in maybe 6 months (most of mine are palatable, but get better closer to or after 1 year). I'd say MINIMUM 6 months, then you may (MAY) be able to bottle, but that's a question that can be answered ONLY when you taste it around that 6 month mark.
Now, as to doing this in a 5g carboy...
You need to primary. That doesn't matter (much) the size of the container. Mead doesn't krausen nearly as much as beer (for the most part..I've had some big ones, and ones that were barely visible).
Then you're going to rack onto fruit, so you'll need a container big enough to store 7# of fruit and your mead.
Then, you're going to rack off the fruit for bulk aging. This is where it will sit for the most amount of time, and headspace needs to be minimal to prevent oxidation and other bad things. If you're going to long term age in a 5g carboy, then you need to plan ahead so that by the time you get to your 3rd carboy - you have about 5g left. Otherwise, you're going to want to top up. Some do that with water. Some do it with a honey/water combo. Some use marbles or aquarium stones to fill space on the bottom of the fermenter (but I think you lose a TON of mead that way unless you're good at racking through the stones to get as much good mead as you can without disturbing the sludge).
I do 5.5-6g batches, knowing that after a racking or two, I'm going to lose enough to be right around the 5g mark.
If you have enough equipment from brewing, here's how I would do it:
5.5g in a 6g carboy (or brewing bucket) primary.
Rack into secondary bucket or 6g carboy for secondary.
5g carboy bulk aging.
I like to use buckets with fruit because it's easier to get fruit chunks out. That and I use the bigger 7g wine bucket so I can put plenty of fruit in and still get 5g of liquid awesomeness into the next racking.
If you must use a smaller primary, I'd tihnk about making it a little higher ABV than you think you want, then when you end up topping up with water, you dilute it back down to the originally planned ABV instead of watering your normal gravity recipe down to an even lower ABV drink.
