Are refugees considered illegal imigrants?

No.

Illegal aliens are foreigners who entered the United States without inspection (EWI), totally under the radar, by climbing over a wall or fence, swimming to US shore, or hiding in the trunk of a car, which is why over 93% of illegal aliens are Mexicans. Somebody arriving in the US with inspection and claiming refugee status is not an illegal alien.

A refugee is defined by the fact that they are moving from their home to due to a danger (or economic hardship) that exists there. By itself, the term does not apply any particular immigration status.

Most non-economic refugees apply for asylum in the countries they move to. If granted, this allows them at least the temporary permission to stay while the dangerous condition persists in their home country, and may offer opportunities for permanent residence. In many countries, a person must be allowed to stay while an application for asylum is processed, even though they could have been turned away at the border. For this reason it is common for refugees to enter a country illegally, before seeking legal status through a claim of asylum.

I'd say that it's generally inappropriate to call refugees who apply for asylum "illegal immigrants," even if they cross the border illegally, because they are seeking a form of legal status and are allowed to stay as part of the law and policy of their host country. This is hardly the same as an immigrant who enters illegally and then simply tries to hide from immigration authorities.

They are illegal immigrants however if genuine they register and make a claim for safe asylum in the country if they are accepted then they become legal either on a temporary basis or more permanent depending on the individual and their needs , if they are denied then they are illegal and are removed or deported as such

No.

Refugees are permitted to enter the USA legally after the Congress okays it.

Yes

No they are allowed to be in the country

Not usually.

they are her legally while their their claims are checked

no, but the 'refugee,' & 'amnesty' rackets are crimes