Depending on the trip and how many portages (and the length) we'll often bring a cooler.  We tend to do trips with minimal portaging and we base camp so it's nice to be able to bring some more creature comforts.  I know I'll likely get mocked for that but to be honest I don't care.  It's nice to have fresh food for a 4 or 5 day trip. It's a total pain hauling a cooler and food pack up into a tree at night though so that's something to consider as well. 

1) Like Uppa said, if you want to head out on Tuesday you need to make a reservation for Tuesday. You can arrive at your destination lake at any time, but if you get there super early there's a chance other campers haven't packed up / left yet. 

2) As you can see from the first few responses, this really comes down to personal preference. Personally, I eat really unhealthy when I trip and eat all shelf stable foods with little to no prep involved. I spend enough time cooking in the city, I don't want to waste hours preparing and cooking food in the backcountry. But most people have the opposite opinion and enjoy the prep/cooking process when tripping. So no cooler for me. Although the group I used to trip with we'd bring coolers with dry ice... incredibly inefficient especially with several km portages but it's what the majority wanted. If you want to bring meat for the first night, just keep it frozen up until you get in the car and it will slowly defrost throughout the day.

3) Can't comment on those lakes, but you could look into Pen Lake as well. Seems to be a popular lake for family trips. One short portage with nice falls in the middle... you can stop at the falls for lunch and one parent stays with the kids while the other carries the gear across. If the older kids wanted to help it wouldn't take long at all, but given how short it is, it would be manageable for you to do alone if needed.

Uppa wrote:

2. I bring burgers for the first night, which ride up in a cooler that never leaves the car, it's just to keep them cold as long as possible. I know plenty of people who bring frozen food in for the first two nights. With a bit of care in wrapping and storing it to stay cold, it's not much of a stretch for food to last that long in the summer. Beyond that you're probably into cooler territory. I don't imagine many people here ever take in a cooler, but I've certainly seen people do so. A very small cooler like those zip-up ones might be reasonably practical as you could hang that without too much trouble. 

Thank you to you and TrippyThings for the idea of frozen meat! Such a simple idea once someone points it out. My husband makes amazing homemade burgers so we will do that for the first night!

I like your planned route/idea for Farm Lake.  From farm, if your older kids are truly adventurous,  you can maybe work your way to the Booth Depot Farm Remnants (probably easier if you stay on the campsite closest to the remnants) - and that particular campsite will give you the feel of being alone on the lake since nobody really paddles by within any kind of range to crowd you in (although I don't know what that site is like).  You can also take a day trip to Booth and paddle around, maybe have lunch at a campsite there.  Booth is a really interesting lake to paddle, the two portages on the way there aren't bad at all, and the first one has a little mini-rapids the kids can ooh and aah at that.   There are several nice sites on Booth for base camping, so maybe you stay on Farm for Day 1, head out to Booth, spend a day or two, back to Farm, then out.

I just got back from a two nighter to burnt island with the family. We carried a cooler bag in with frozen steaks and bacon and a bunch of veggies.  I wouldn’t recommend it for long portages, but it wasn’t bad for the short ones in between Canoe and Burnt. Hanging it was fine. I usually just put all my food into a dry bag and hang that. Keeps things dry if it rains and I like to tell myself it keeps the smell of the food contained.