If we hold ourselves to be against the capitalist system, isn't it utterly hypocritical to use Twitter and IPhones to communicate, considering how both of those were created by capitalists?

Capitalists created nothing. Capitalists are the class of people that don't create anything physically and just come around managing the workforce of people that actually do. Workers created Twitter and iPhone.

Even I think it's a bit of a stretch to say that the internet wouldn't exist without capitalism, but do you think the same?

Taking by the example given by someone in this sub once, when the CEO of Comcast is laying Internet cables around, programming by himself all the internal structure of his service, then you can say Capitalism provides us with Internet. Until then, it will be programmers, engineers, the people in the factories that manufacture Routers and those who risk their lives working in utility poles.

Is the problem really just Corporatism because doesn't capitalism readily produce monopolies and corporations?

There's no such thing as Capitalism without Monopoly. It's an inseparable characteristic of this system and it will never go away.

If Capitalism needs minimal regulations to not produce monopolies, which guarantee do you give that this "minimal regulation", call it small goverment or whatever you like, will not be a monopoly by itself ?

After all, to reach common agreement in the free market, so it can create self-regulations, orders need to come from some place. It needs hierarchy. It will follow the lead of a single set of people. Who is to say that they will not represent their own interests instead of the interests of "free market" ?

Isn't the reason why corporations lobby for more government intervention is because they just want them to destroy their competitors, and if so, should we be more against larger governments?

So Corporations come around and fill the vacuum left by the Government themselves ? Nope. I will pass on that. The State is a Burgeoise institution already, but nothing is worse than Corporatocracy.