Can customers buy in increments (eg. buy 5 for $X, buy 10 for $Y, etc.)?

Yes, they can, it just requires a bit of theme modification.  You can modify your theme to do this by following these steps:

1. From "Shopify Admin", select Online Store.

    

2. Select Actions.

    

3. Select Edit code.

    

4. Under "Templates", select product.liquid.

   Note: If your theme contains sections, you may have to make these changes in a different file, like product-template.liquid under "Sections".

    

5. Find the quantity box code like this:

   Note: Some themes, like Radiance, do not have a quantity box. If yours doesn't, you can skip this step.

    

6. Replace with this code:

   <label for="quantity">Quantity:</label> 
   <select id="quantity" name="quantity">
   {% for i in (1..10) %}
   <option value="{{ i | times: 1 }}">{{ i | times: 1 }}</option>
   {% endfor %}
   </select>

    

7. Select Save.

    

That's it!

This code will create a drop down list of the numbers 1 through 10. To customize this code:

{% for i in (1..10%} controls the number of selectable options in the drop downs.

<option value="{{ i | times: 1 }}">{{ i | times: 1 }}</option>

Change the 1 to the number of increments in your discount. So if your discounts change in increments of 25, you would change the 1 to 25.