Is it beneficial to have a Research Lab on every colony?
Not really. You can only have one research going at any given time, regardless of how many Research Labs you have.
One or two reasearch plants are ok. Since you may be able to research at ColonyX while building a new Solar Plant at ColonyZ. But each colony doesn’t needs a research plant. Especially if it has a low qty of fields. Save those fields for resource production.
Research is universal. If you research Energy Tech 7, then all your planets have Energy Tech 7. However, if you need to use that technology in building defenses, or ships or such, you still need all the requirements for that defense or building or ship.
So if you have everything to build Heavy Lasers on ColonyA, and you create ColonyB, you need the appropriate level Shipyard before Heavy Lasers show up as on option.