How do I remove taxes and shipping cost for wholesaler customers?

You can use the override feature to exempt your wholesalers from taxes and shipping costs, or to define fixed cost for wholesalers. To do that, you simply need to enter the tab Discount Groups in Wholesaler admin and select the Discount you want to change. 

For taxes, you can use the Tax exempt option:

This will not change the price the customer sees, but it will adjust Shopify invoices of your store not to include taxes in them. Heads up! be sure to define the prices without taxes for wholesalers in this group!

For shipping, you can specify a flat amount to be paid by the wholesaler instead of the calculated shipping from Shopify:

Setting Shipping price to 0 will "force" free shipping to this group.