Budget and space are genuinely limiting factors, and we can't just snap our fingers, pray or buy lottery tickets and solve that. Half the thought in this hobby goes into finding ways to ignore the limits space imposes on our aquarium ambitions. But you asked very pointed questions. I'll give you my answers, which you can accept or reject.
1. Are red “honey” gourami actually honey gourami with just a different colour strain?
Both, and neither. The trade name in English can be applied to 3 creatures, as already mentioned. It could be labiosa, chuna or a cross. It can also be labiosa treated with hormones, in which case the red will fade. In the marketing of aquarium fish, some English names are used for several different fish, or one fish can have a whole list of trade names...
2. Do the rules for honey gourami apply to the red “honey” gourami?
Probably not. If it is labiosa, it's a bigger fish in time. It's more aggressive than chuna.
3. Do these red “honey” gourami get bigger than the honey?
Double the size. I've seen some quite large ones.
4. Is a 6 gallon a good size for a single red “honey” gourami?
No. Bettas hover and are ambush predators. Honeys swim around and need more space. They're both anabantoids, but it ends there. You can keep a honey alive in a 6 with steady maintenance, but it isn't ideal. If it's a labiosa, the space will be very tight.
5. Would adding 6 to 8 chilli rasboras be a good idea?
Absolutely not, in a tank that size. If it were an 80ltr, I'd say yes.
6. Are the red “honey” gourami peaceful like the honey?
It's relative. I bred T chuna for quite some time, and they were peaceful fish if they had room to get out of each others' way. They were real honeys. T labiosa are rougher characters, and when the very red morphs were developed, I think the "honey gourami" name was hijacked so aquarists would buy them thinking they were the more peaceful and gentle cousin.