Hi Mickey! Yes, some plants give off more oxygen than others, but it’s mostly proportional to size. Larger plants give off more oxygen than smaller plants, so the biggest oxygen producers are trees. Also, faster-growing plants give off more oxygen than their slower-growing counterparts. Light plays an additional factor. If there are two identical plants, but one is receiving more light, the one receiving more light will give off more oxygen. Think of the plant as a machine. The more materials put into the plant (water, nutrients, light), the more product it will create (oxygen).

To answer your second question, oxygen, glucose, and water are the only byproducts of photosynthesis. The oxygen is released into the air, the water is reused by the plant or released as water vapor, and glucose is used or stored for energy by the plant.

A common misconception is that plants stop photosynthesizing at night. This is untrue. The plants take the oxygen and glucose produced during the day and undergo cellular respiration, turning them into carbohydrates that are essential for the plant’s growth. This happens at an equal or even faster rate at night than during the day.

In order to get carbon, plants need to produce oxygen as a byproduct. This is a simple matter of chemistry: carbon dioxide and water make oxygen and sugar, and the oxygen has to go somewhere, so the plant outgasses it.

Some plants can do photosynthesis more rapidly than others, and some plants can do photosynthesis with less water or light than others, but all plants use the same chemical reaction that produces sugar and oxygen. Thus, the ratio is always the same.

All of this said, while there are no plants that produce something other than oxygen by photosynthesis, there are some bacteria that produce sulfur in place of oxygen, since they use hydrogen sulfide in the reaction in place of water.

The following link contains valuable information for you:
Microscopic plants [phytoplankton] in the ocean produce half the oxygen on earth!

The oxygen is produced by photosynthesis.

You may be wanting to know about improving the quality of indoor air. Snake Plant [Sansevieria trifasciata or 'Mother-in-Law's Tongue'] is supposed to produce lots of oxygen, but plants supposedly don't give off enough oxygen to change the air in your home.

Here's one of the 37 review articles about plants and air quality in 2018-2019. I chose it, because I think the 'Trends in...' journals have a good scientific reputation. Plants for Sustainable Improvement of Indoor Air Quality
Trends in Plant Science, Volume 23, Issue 6, June 2018, Pages 507-512

It says we need smart sensors in buildings and more research on what plants are good for the air, not just what plants are nice to look at.