Even though 'zullen' is used in everyday language it is not an official verb. For writing official texts it should be avoided and replaced with 'willen' (want), 'gaan' (go or will), zin hebben om (do fancy/would like to) or 'kunnen' (can). For example the informal sentence 'zullen we gaan vissen?'/Shall we go fishing? Becomes: 'Heb je zin om te gaan vissen?'/Do you want to go fishing? 

'Zullen we....' therefor becomes 'Heb je zin om....''. For a more formal way of asking you can use 'Heeft u zin om...'

The past tense for zullen 'zouden' is used in settings where you depend on the other person, for example: "We zouden uit eten kunnen gaan?'' Eventhough the past tense is used here it means ''If you are willing we could go out for dinner.'' The past tense softens the verb from a direct request to leaving the option to the other person entirely. 

I'm not sure about this, but i would not be surprised if 'zouden' is the irregular past tense of 'kunnen', from which 'zullen' later became a derivative from for the present tense. Or it is a dialect form for 'willen' of which the past tense is 'wilden' or 'wouden'. The first used more often. In ABN (General wellspoken dutch)  'zullen' is seen as child's speach.