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Sure! This article will give you a rundown of the care that they require: https://www.gardeningknowhow.com/ornamental/flowers/peony/peony-care.htm

Bulbs alone generally can't be identified. You may need to wait for blooms to correctly id them.

This appears to be iron deficiency with the typical green leaf veins and yellow between veins. Chlorosis doesn't usually have this pronounced difference between vein color and leaf color. A soil test is the only way to know for sure which deficiencies you have; pH can also affect whether the plant can take up elements like iron. If you decide to do testing yourself and not use a laboratory, follow the instructions exactly to get accurate results. Iron sulfate is a product that lowers pH (sulphur) and provides iron. Correcting these deficiencies doesn't happen quickly as soil micro-organisms are involved in the process. But supplements this fall should be noticeable in next year's growth.

This article explains how to divide peonies.

https://www.gardeningknowhow.com/ornamental/flowers/peony/dividing-peony-plants.htm

Only cut back to shape the tree or remove dead, damaged or diseased wood. See the article below for instructions to fertilize:

https://www.gardeningknowhow.com/ornamental/flowers/peony/how-to-grow-a-tree-peony.htm.

Prevention is the best course for treating fungal diseases. Clean up any leaf litter around the plant to reduce the spores overwintering. Trim off the leaves and discard in trash. It should return next spring. You may want to contact the local extension office to be sure it isn't a virus, which it would not survive.

Here are more tips and disease analysis.
https://www.gardeningknowhow.com/ornamental/flowers/peony/treating-spotted-peony-leaves.htm