Drain line into 3" stack

I had a shower tray backing up when water was drained out of the bath tub next to it. Plumber came by and used one of those little hand held motorized drain augers. He was able to pull up enough hair and ROOTS to get the drain working again. But would this little auger do as good a job as one of those $500 1/34 horse power drain machines with the C-shaped cutter (like this one [url]https://contentgrid.homedepot-static.com/hdus/en_US/DTCCOMNEW/fetch/Enterprise/Tool_and_Truck_Rental/Plumbing_Equipment_Rental/drain-cleaner-100x5-8.jpg[/url] )? House was built in 1956 so I'm assuming that it's cast iron pipes down there. Right? After talking to neighbors and the top leak detection expert in my area I've decided for now to try to just control the roots with foaming root killer, I took out a suspected plant that may be feeding the roots, and I could do preventative drain cleanings. Any thoughts? I was thinking about buying one of these machines. What attachment would I need? [url]https://www.homedepot.com/p/RIDGID-115-Volt-K-400-Drain-Cleaning-Drum-Machine-with-C-32-3-8-in-Integral-Wound-Cable-and-Tool-Set-52363/206405033[/url]

I realize that someone here is going to say hire a professional, but unfortunately that is not an option at this time, but the job still need to get done. So I would appreciate any help with this from anyone that is familiar with the code. I'm installing a basement bathroom. There is one currently roughed in, but it is in a location that is just not practical and it would only service a sink / toilet. I need to have a bath tub / shower as well so I had to move it. I've drawn up the existing layout (drains-existing.jpg). The stack on the left side has a toilet straight above and there is a vent that is going out as well which goes upstairs and into the roof. I will be tying my vents into that one (for anything that you see as vents on my drawing). I need to know if this would be according to Ontairo building code. I think it would work, but I want to be sure before I change/install any new pipes. The concrete is already broken and trenches dug. I'm basically ready to install the drain pipes. I did the best I could to draw it in photoshop. The existing plumbing has a Y (wye) fitting that connects the floor drain and the waste stack and then goes out to tap into the sewer line I guess. I basically just want to change the wye fitting to a double 45 wye fitting thereby giving me a third branch off to the right which will handle the toilet and bath tub (the red lines show where I would vent it -- I assumed that because it is within 10 feet that it would be okay to vent both the tub and the toilet). The middle branch for the wye adapter would go to drain the sink which I would vent with a tee adapter (vertically). I would then cap off the floor drain line that is there now and fill it with concrete. Instead I would install a new floor drain to the left of the wall (green line) which will be a small hallway. My thought process on moving the floor drain is because the water heater (and furnace) will be behind the bathroom (above where the text is). So, if the water heater went or something, then the water "should" go around the bathroom and eventually go into the floor drain. For that I would put a new Wye fitting into the line that is already there between the waste stack on the left and the double wye fitting. I would really appreciate any helpful comments! Thanks in advance.