Would he be able to defeat Gutts?
Depends on who is writing the story
/every powerlevel thread ever
No, because Beserk is not crap.
You can't use a blade to kill a blade made to break blades.
His sister could kill them both at the same time.
This does not apply here, and this isn't a powerlevel thread because it's only 2 dudes.
Probably. He'd be able to take out a majority of sword fighters that aren't in "i blewd up planet" level or higher.
Can Archer project Shichika?
I bet Shiki can kill them all.
Shiki, SHIKI, Shiki, Shiki, SHIKI, or 「 」?
Hes a Nisio Isin character which means his hypothetical powerlevel fluctuates depending on the direction the author wants the series to go. If Nisio Isin were writing this supposed fanfic Shichika would win for sure, if he wasn't it may be a bit more sketchy but I'd say Shichika would still win just because the nature of his power is kind of bullshit.