I can't see why you wouldn't be allowed into Nyika on a bike. Locals use motorbikes and push bikes to get around and most of the road in from the gate is a public highway.

The tracks will vary given the time of year and regularity of use. In the rains you can get deep mud on the way up there and it can be very slippy. Plus there are some rough patches (rocky and/or water erosion). The roads on the plateau would be stunning on a bike (very few vehicles and stunning scenery) but again some are what I would call "off road" ie rocky. It depends what your bike is capable of. I would guess if you go slow and careful you'd be OK most places, most times of the year (sorry I don't ride a bike). The "main" tracks will be fine I'm sure. They should be graded.

Vwaza is a great park to visit and you could easily get there on a bike but there isn't much scope to drive around (in a car or a bike). And there's no need as the lodging/campsites are at Lake Kazuni which is where the animals all congregate. It's a massively underated park and I'd encourage you to go. However, the deal is you drive 500m to the lake and pretty much stick there (you can do guided walks). In the dry season especially there are a lot of elephant and they are not friendly. You really wouldn't want to meet some in the bush on a bike.

Nkhotakota would I'm sure be allowed too. A rough dirt track in but it's only 20km or so. You are unlikely to see any game but it's a fabulous spot to stay at Bua River. Again no real scope for driving around.

Liwonde - you'd have to check. The concern will be elephant I think. Most elephant in Malawi are jittery and more likely to charge/chase than in many other African countries. You hear of people being trampled on a fairly regular basis. The locals I lived among were terrified of them (we would sometimes have people follow us on motorbikes when we went in and out of the park - for "protection").

Majete will be the same - they may have a concern about the elephants.

If I were you I'd contact some of the operators in the parks. Pretend you may be coming to stay at their lodge and ask if you can arrive by bike. If they say yes print out the email to show at the gate in case they aren't sure. But generally parks are much more low key in Malawi and they are much less rules orientated than say Zambia, Botswana, Kenya. But that's because there are no dangerous cats for them to worry about. They are also much cheaper than anywhere else ($10pppd).

You're more likely to get deep sand around the lake - ie on tracks leading to campsites lodges from the main road - but it won't be for much distance. Worst case scenario get off and push I'd think.

Thank you very much for all your info. Rocky parts are perfectly o.k., the only thing which gets difficult is deep sand with both of us on the bike. For short distances my wife might prefer walking anyway...

Elephants generally love bikes, we almost got hunted down by one last year in Zambia. We will check carefully.