My husband and I own a business together (50/50) but I am the only one actively working on this business. Can I just enter all of our business deductions on my portion?

No.

You can deduct any necessary and ordinary expenses of the business.  

I do not know what kind of business you own, but many businesses have silent partners so as long as the business needs the expense, you can deduct it.  

Obviously, if it is just a personal expense for your spouse, then you cannot deduct it.  

Example, your spouse has a phone that he never uses for business, that cannot be a business expense.  

Example: You bought tools you thought your spouse would use in the business that are not being used now, you can still deduct those because they belong to the company.

For common expenses, see below. 

https://turbotax.intuit.com/tax-tips/small-business-taxes/taking-business-tax-deductions/L5RueYPVS

Thank you. What about Vehicle expenses? Do I have to split that one on Schedule-C as well?

Only claim the miles driven for business if you use the standard mileage rate.  If you use actual expenses, you can add them all in.  If you use your car for our spouse or not exclusively for business, you need to assign a percentage of the time you use your car for business and multiply that percentage times your car expenses.
I will include a link because that gets a bit complicated.
<a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tips/small-business-taxes/business-use-of-vehicles/L6hi0zzzh">https://turbotax.intuit.com/tax-tips/small-business-taxes/business-use-of-vehicles/L6hi0zzzh</a>

If I chose Standard Millage Rate and I kept track of my millages, do I still need to split the millage 50/50 with my husband, if we own this business together(50/50)?

no.