You are correct about both sentences.
In the 1st sentence the grammatical mistake (if there is one) is the use of that instead of which. The use of tropical in place of financial is a possible factual mistake, which a student of English might not be expected to know, but it is not a grammatical mistake which a student of English ought to know.
The American blogger in Writers' Digest suggests the following test :
If the sentence doesn’t need the clause that the word in question is connecting, use which. If it does, use that.
The first clause can stand by itself ("Oil is an important tropical material") without losing or altering the meaning. So according to American English usage we should use which here. It should also be preceded by a comma :
Oil is an important tropical material, which can be processed into many different products.
Such a non-essential use is termed non-restrictive. However, as Clare implies in a comment, in this sentence it is also possible to interpret the subordinate clause as being essential information which is required to identify which kind of the many important tropical materials oil is. Such a restrictive interpretation requires the use of that in American English. A slight alteration makes this clearer :
Oil is one of the important tropical materials that can be processed into many different products.
In British English the use of which (without a preceding comma) in place of that is accepted in such restrictive cases. See Oxford Living Dictionaries.
Oil is an important tropical material which can be processed into many different products.
In the 2nd sentence the word "do" is not required. "What do you mean?" is a sentence on its own :
"I'm sorry, I cannot see. What do you mean?"