Are the above sentences correct?

A lot of excess, in general, making the sentences unnecessarily complex.

If John tried to removed that belief from her head, what he'd be really doing would be to removing himself.

I think your second sentence is correct as written, but better wait for the more expert opinions.

As for the other two, this is how I would re-write them, staying as close as I can to your model:

If John tried to remove that belief from her head, he'd really be removing himself.

This kind of laughter could mean he was overflowing with joy or overwhelmed with desperation.

Quilliam said:

If John tried to remove that belief from her head, what he'd be really doing would be to remove himself.

The green paper seemed to curve for forever towards her.

It was the kind of laughter that could be interpreted as if he was either overflowed with joy or overwhelmed with desperation.

Click to expand...

If John removed that belief, he'd really be removing himself. (Or: If John tried to remove that belief, he'd be really be trying to remove himself.)

The green paper seemed to curve forever towards her.

His laughter could be interpreted as either overflowed with joy or overwhelmed with desperation.

Third sentence:

His laughter was either overflowing with joy or overwhelmed by desperation.

Let the audience decide.

The sentences appear below the question, not above it.

More extensive edits are possible and probably desirable, but this is the minimum to make it grammatical.

Quilliam said:

If John tried to remove that belief from her head, what he'd be really doing would be to remove removing himself.

The green paper seemed to curve for forever towards her.

It was the kind of laughter that could be interpreted as if he was either overflowed overflowing with joy or overwhelmed with desperation.

Click to expand...

As a more general comment, it's almost always useful, when you have a sentence that is bothering you, to consider rephrasing it rather than overworrying about its grammatical correctness. Grammatically correct sentences can often be perfect festering horrors in terms of clarity, style and effectiveness.

caw

What blacbird said. I've read entire manuscripts that had nary a grammar or punctuation error, and they were horrible. Grammar and punctuation are only a small part of what makes a sentence good. A good sentence need rhythm and flow, perfect word choice, and can sing better than Sinatra in his prime.

Quilliam said:

If John tried to remove that belief from her head, what he'd be really doing would be to remove himself.

The green paper seemed to curve for forever towards her.

It was the kind of laughter that could be interpreted as if he was either overflowed with joy or overwhelmed with desperation.

Click to expand...

1. In removing that belief from her head, John would be removing himself.

Or If John removed that belief from her head, he'd have to remove himself.

2. The green paper seemed to curve for forever towards her.

No idea what that means, but--

The green paper seemed to curve endlessly towards her.

3. It was the kind of laughter that could be interpreted as if he either overflowed with joy [or, was overflowing with joy] or was overwhelmed with desperation.

That makes it grammatically correct, but it's still kind of clunky. Could it not be simplified?

He laughed, either from overflowing joy or overwhelming desperation.