Is it possible for illegals to pay taxes, is there some special form for that?

Yes, it is possible, but there is no special form needed.  They can use the same tax form as everyone else.  The only difference in the forms is that instead of using a Social Security Number, they have to use an Individual Taxpayer Identification Number.  I suppose, if you want to be technical, there is one special form, which is the form to apply for the Individual Taxpayer Identification Number.

It is almost possible for them not pay more taxes than citizens, because they get hit with the same tax rates but don't qualify for the earned income credit.

They can apply for ITIN numbers through the IRS to file returns but in many cases they get more back in EITC and child tax credits than they pay into the system. 

Yes, it is possible for an illegal alien to pay taxes.  They have to request an ITIN (individual taxpayer identification number) so substitute for a social security number. Once they have it they can file an income tax return. Do you actually think a noticeable number of illegal aliens do that?

They are REQUIRED to pay taxes. Breaking one law does not give you a pass to break other laws. There is no special form. Employers of illegals are required to file the same payroll tax forms as they do for legal employees.

Very possible.  And a majority of them do.  Check this out:

IRS estimates that about 6 million unauthorized immigrants file individual income tax returns each year. Research reviewed by the nonpartisan Congressional Budget Office indicates that between 50 percent and 75 percent of unauthorized immigrants pay federal, state, and local taxes.

Economic impact of illegal immigrants in the United States ...[https://en.wikipedia.org/wiki/Economic_impact_of_i...

Can't be positive about the form used.  But I do know that they are not required to disclose their immigration status when filing.

Yes. Their employers pay the Taxes out of the pay. Every year the irs collects money that nobody claims. Sometimes it’s millions extra.