I have a 16GB memory card that I got while purchasing the camera. But I also have an EVO Plus 32GB microSDHC card in my mobile. Is there any issue using this card with an adapter in my camera?
There shouldn't be an issue (the camera shouldn't be able to discern between a regular SD card and a micro SD in an adapter), just be aware that the camera might want you to format the card (and even if it doesn't, it's a good practice to do so), hence you will lose any data you may have on the card. You might need to format it again when you put it back in the phone.
SD cards are generally interchangeable (with adapters). Their performance characteristics vary. SD card class is a rating for writes and the minimum requirements will depend on the application.
For video, write speed matters significantly and higher resolutions require higher write speeds.
For normal photography, write speed will tend to be less critical. Modern cameras have a buffer and can hold a meaningful number of shots when shooting burst mode. Image format effects the number of shots the buffer will hold: fewer RAW format images, more Jpeg images. The occasions when the write speed of the card are likely to matter are sequential bursts of photos.
My advice is to try it out and see if it works in the situations that you normally take photographs...but maybe not when those situations are critical. On the other hand, a good high quality reserve card may offer piece of mind to justify the cost. Again, it's a matter of the reasons for taking the photographs.