1

There's no way to get to Madagascar from Moz, you will have to fly from Jo'burg.

2

Naivasha is near Nairobi, less than 2 hours drive. It's possible to go to Naivasha in the morning and go back to Nairobi and take an evening/night bus to Kampala.

3

That's a very ambitious trip - are you giving yourself enough time? I reckon you'll need several weeks/months to do this.
When we were in the area Burundi was a no go zone, things maybe changed but I'd check carefully before you go.
Getting down the Western side of Tanzania From Rwanda/Burundi to Malawi will be difficult. Consider the MV Liemba which is a ferry that runs down Lake Tanganyika - we caught it from Kigoma in Tanzania to Mpulungu in Zambia - and it's an awesome trip. I think it also stops in Burundi - so that might be an option too. I think you'll struggle to get public transport via roads to connect those dots otherwise (alternatively head towards Dar)
Been through a few Mozambique/Malawi borders and wouldn't foresee a problem.
Note that Maputo back to Dar Es Salaam is also via Malawi and a LONG way - as far as I know there aren't very many options to cross the border from the North of Mozambique into the South of Tanzania, though I might be mistaken.

4

This seems much too rushed, offhand, starting with the idea of heading up to Naivasha for a daytrip. Reading between the lines you want to visit Uganda for three days, Rwanda for two, and transit through Burundi, Tanzania and Malawi and Mozambique on your way to Madagascar for "a few days," after which you would head back north for the flight out. Whew!

Maybe I have it wrong and you simply didn't include any detail on the later countries. But you need much longer than you've hinted at here for this kind of trip.

I assume this is not a first-time trip to the region.

1. Yes but it'd be rushed. Are you just flying to Nairobi and then immediately leaving for Uganda?

2. You can get anywhere you like in stages, whether there is direct transport or not.

3. Yes it is possible to get to Tanzania from Burundi, though it used to be slow going (this may have changed). I have not made that crossing.

4. There is more than one crossing from Malawi to Mozambique. The one at Nayuchi/Entre Lagos allows easy access to the train east from Cuamba, but you may likely want a different one.

5

The only advice i can give the border between malawi and Mozambique is passable by road and there is public transport for but once you get into Mozambique things get a bit difficult because of even communication English is very rarely used there i have travelled in that route from capetown to nairobi but especially mozambique is a difficult country. I wish safe journey

6

Hi Burundi is more secure than before now, if you want more details check out this website www.bujumburaflightsstats.com

7

Here are my questions.

1. Would I be able to leave Nairobi early in the morning to Naivasha and Hell's gate and be able to return back to Nairobi to catch a bus to Uganda? I do not plan on saying overnight in Naivasha.
yes you can Nairobi- Naivsha is 2 hr drive and then book the 10pm bus to kampala. You may even see if Kampala coach will pick you up in Naivasha since itsenroute to the border.

2. Would I get a bus from the Lake Victoria area to the Rwandan border?
Kampala coach goes to Rwanda and Burundi from Kampala