Insure also means to guarantee against financial loss. Though ensure is preferable, you can use insure , but be consistent. A compliment is a remark of esteem, praise, or affection. A complement is something that fills up or completes another. Outside of the thesis acknowledgments, complement will probably be the correct term.
Data therefore takes a plural verb.
Both are followed by commas. The punctuation preceding these could be a comma, semicolon, or dash, depending on the magnitude of the break in continuity. Because theses and dissertations are formal documents, you should avoid contractions such as this. Lay takes a direct object, lie does not. If you are unsure which verb to use, try using place or rest in place of the verb to see which meaning fits.