Buredoran's third form is called Buredo-RUN. The Matrintis are machine based, and RUN was the code used in the BASIC computer language to run applications.
Why do mecha get introduced in relatively quick succession within the Warstar arc? Because it's structured like a miniature version of Sentai arcs, complete with a Super Daibouken-esque mecha in the form of Hyper Gosei Great.
Not really Fridge Brilliance. Since Shinkenger teamed up with Decade and the fact that they are each other's Super Hero Time counterpart, it is only logical that W will be Goseiger's counterpart followed by OOO and Gokaiger and so on.
Preemptively addressed with Gosei Knight - obviously he can't be shown pressing the Leon Cellular when he's in Headder form, so we see it floating in Hammer Space with the buttons responding to his thoughts.
Speaking of the Leon Cellular, why is it shaped like a cell phone? This raises all manner of questions and issues:
Now, Presumably the logic behind most cases of cellphone morphers is that humans can carry it around with them at all times and use its communicator function freely without attracting attention from passerby other than "hey, cool phone". That's all well and good, but Gosei Knight doesn't look like a human, so disguising his morpher is the least of his concerns when it comes to attracting attention.
Also, why does he even need to enter a code on the keypad to use his cards? The Goseigers' tensouders didn't need any input other than the cards themselves (and maybe some voice commands) in order to activate, so why does the Leon Cellular require a keypad combo? It would make sense if he could activate different functions of the same card by entering different codes, but he never does that.
And come to think of it, why does he even use cards in the first place? It was mentioned that tensou cards and tensouders hadn't been invented back when Gosei Knight was last active 10,000 years ago as Groundion Headder, and he spent that 10,000 years frozen in ice and cut off from everything except sensing the earth's life force. How would he even know what tensou cards were, let alone cellphones?