What is the expected size of the plasmid plus the cut foreign dna? 2. what type of ends do the enzymes bamhi and ecori produce? how does this type of end facilitate cloning? 3. what enzyme is necessary to permanently link the digested foreign and plasmid dna together to form the recombinant dna molecule? how does this enzyme work?

The size of the plasmid can be up to 200kbp, you can blast the sequence to determine which plasmid it is and what is its length. This way you can subtract the length from the total length of the plasmid to calculate the length of the foreign DNA insert.
The enzymes EcoRI and BamHI produce 'sticky ends'. This means that the single stranded ends at the terminal can be joined due to complementary bases.
The enzyme is known as DNA ligase, it works by forming a bond between the phosphate group on one strand and the deoxyribose group on the strand it is being joined with.

Hope that answers the question, have a great day!