The main idea of a paragraph is introduced in the first sentence of the paragraph (which is called the topic sentence), and the rest of the paragraph would be about the topic sentence. So, if the sentences you wrote are the topic sentences of two separate paragraphs, the rest of their paragraphs would be about them. The topic sentence has a general tone ...
The subject of the sentence is we. The topic (what the sentence is about) is exploring Spain on a bike tour. The controlling idea is "Only open to those who really want to visit the three regions mentioned".
B) I will be traveling and eating on Monday and Tuesday.
The construction that you want is:
On Monday and Tuesday, I will be traveling and eating.
A fronting adverbial is a free modifier and modifies the entire clause (or clauses where there is more than one equal clause.)
"Me". You can judge this by considering the following different ways to say what you mean: "it will be just us" and "it will be just we". Now if "we" sounds wrong to you, then "I and you" should also sound wrong and for the same reason: the pronouns "we" and "I" are in subject case. So if ...
Until the question is closed (it is a duplicate of Is "data" treated as singular or plural in formal contexts?), consider this:
Data singular or plural is now a matter of choice.
Data is the Latin plural of datum, so your teacher is fundamentally wrong.
However, usage has shifted because of general ignorance of Latin, to use data as singular.