the warp gates don't seem to be able to transport modded items
my upgraded radars (Big Brother 2.0) get left behind when I pick up the mining platform (or warp dimensions and it gets automatically recalled), my tiered spidertron can't even use the gate, and the belt balancers from Belt Balancer 2.0 crash the game when the mining platform interacts with them

So, for the radar it comes from the fact the radio tower is a radar and is excluded from the recall of harvesters, so "any" radar will fall in the same logic actually.
Spidertron in harvesters are not recalled as well, as if it's not correctly inside the harvesters (some legs in, some out) it'll "half" teleport the spidertron, and break it. But I can't really remember why i prevented vehicles (cars, spidertron, etc) to teleport in the base, i'd need to have a look to that and improve the teleport process.

For belt balancer 2 (i believe this mod: https://mods.factorio.com/mod/belt-balancer-2 ) i'll need more details like, what do you mean by "crash the game" ? You get an error ? What do you exactly do ? How can I replicate the issue ?

Keep in mind that any mod that change loaders and linked-belt may break the mod.

yes, that mod
when you try to pick up a platform with a balancer on it you get this error:
The mod Belt Balancer 2 (2.0.9) caused a non-recoverable error.
Please report this error to the mod author.

Error while running event belt-balancer-2::on_nth_tick(4)
LuaTransportLine API call when LuaTransportLine was invalid.
stack traceback:
[C]: in function 'len'
__belt-balancer-2/objects/balancer.lua:203: in function 'run'
belt-balancer-2/helper/message-handler.lua:33: in function <belt-balancer-2/helper/message-handler.lua:31>

as for the spidertron, it won't go through any of the portals either base to outside or base levels up and down, though you seem to indicate that this is variant on intended behavior