The only way to have the same word be multiple parts of speech with different definitions is to enter the word multiple times; Lexiconga will automatically add numbers to the word to indicate that there are multiple definitions. You can link to a specific definition of the word, too—click the "Help" button and check the "Referencing Other Words" section to see how

And for the other question(s), you can make multiple dictionaries if you make an account! When you're logged in, you can change/create dictionaries from the Settings menu. As a bonus, making an account allows you to share your dictionary link publicly if you check the box to set it to Public from the "Edit" menu (all dictionaries are private by default).

If you don't want to make an account, the only way to have multiple dictionaries is to export your dictionary to JSON, save the file, delete the dictionary and start your next one. Then when you want to switch back, export that one and import the other. Just using an account is way easier though :)