Can I use throttled Internet (32kb / s) in the menu of Fortnite Mobile, so also in the item shop, or do I need for data volume?
If it is ensured that your mobile service provider does not automatically add additional data volume when using the Internet with throttled access (data automatic), you should definitely come into the game menu and the in-game shop with the appropriate patience.
In the worst case, the game server aborts the request because of too long data exchange.
At 128 kbps I can usually do a lot (with patience) on the web and even play various online simulation games. (for direct games, you are not even here for the game mentioned)