Taperava, first of all, let me thank you for your questions. I will answer the easy one first. To keep the thread from coming loose or being pulled into the bobbin, always hold the thread tails when you start sewing. Let go after a couple of stitches. When doing alot of piecing, such as squares together, do not remove each piece, but rather butt the next pair against the finished pair and keep sewing. This form of production sewing saves on thread and time. I take my line of sewn blocks to ironing board and clip them apart as I press the seams. You can also end with a folded scrap, so the thread is still engaged. Just clip last block from that scrap, while leaving the scrap in the machine. Then when you sit down to sew next batch, just butt it against that scrap piece and keep going.
Ensuring square blocks is not difficult with a square up ruler. I have many sizes, and use the ruler closest to size of intended block. Sometimes, you can luck out and have a ruler and block the same size. Either way, you will begin by cutting a strip the width of the square you need. Using your ruler, line up the top and bottom, top on the edge of strip width, and bottom on the line of the square size. The it just a matter of cutting one side. The size of the block should be lined up with the lines on the ruler. For example, if cutting a 4" block, 1st cut a strip 4" wide the width of fabric. At this point you will have a strip 4" by 40-45". Cut the selvage off using your ruler so you can be sure it is straight. At this point, you now have three sides of your block already cut. I would then take my 6" square up, line up one side against the top of strip, bottom should line up on the 4" line, and move the ruler until the edge lines up with 4" line on the side. Engage your rotary cutter, keeping fingers out of way! That one cut will be repeated until you can no longer make a 4" square on that strip. You will now have 40 4" squares which will finish as 3.5" sq. when sewn.
I hope you find this information helpful. Let us know if we can help you with any other questions.