A normal frying pan can work as a wok but its best to use a very deep frying pan that is at least 1 and a half inches deep.
Woks rely on oil and high heat to cook meat and vegetables and if you use a shallow pan, grease will get all over and might even spill out and start on fire. That’s no good at all.
For rice, a normal saucepan will work but you need to make sure you have a tight fitting lid. Tin foil over the top will work in an emergency but can burn you and is not recommended.
Many Chinese recipes call for a meat or seafood to be breaded and deep fried. Without a deep fryer, you are going to have a mess no matter what.
The deepest cooking pot or saucepan you have will work but will probably splash all over no matter how you try to contain it.
These are basic solutions but having the proper equipment can really make a difference. An electric wok is very easy to clean and can also be used to deep fry.
A rice cooker really isn’t necessary unless you truly can’t cook rice. Buy what you need and have fun with your new recipes.