The plural tombeaux can’t be used to refer to a single tomb. Of course, the singular tombeau does.

Research is uncountable in modern English so almost never used in the plural¹, while both recherche and tombeau can be used both in the singular and the plural.

While tombeau poses no problem, for recherche we have:

• La recherche which is similar to the English “research” when used generically, i.e. the research field/domain.

• Des/les recherches which represents a collection of distinct research activities, i.e. pieces of research. It is also usually translated to “research”.

Even if there is a single piece of research, e.g. “my research about squaring the circle”, we often prefer the plural:

• Mes recherches sur la quadrature du cercle is common
• Ma recherche sur la quadrature du cercle is rare

The singular would be used with:

• Mon étude sur la quadrature du cercle

¹ _{That wasn’t the case until the 20th century. Earlier,
researches used to be prevalent.}

No, it can’t. But the singular of “tombeaux” is “tombeau” (and not “tombal“, which is an adjective). They sound the same, maybe that why you’re confused.

For “research”, it can translate to “des recherches“, but that’s when it’s uncountable in English.