My wife has a single-member LLC company. We filed K-1 last year via a CPA. Can we file Turbo-Tax self-employment this year instead of K1? How about Texas filing for biz?

If a CPA filed a form 1065 with 2 schedule K-1s, then your business must have been a multi-member LLC. As long as you've dissolved your multi-member LLC and formed a single-member LLC, than yes, you can use TurboTax Self-Employed for your wife's business. 

You simply add her business under the self-employed section and you file it with your personal returns (no k-1s involved!)

If you had a partnership, you should file your final year return. If your tax preparer made a mistake last year, then you could amend it. Partnerships can be handled in TurboTax Business software as well (which does not do individual income tax forms). 

Texas has no income tax return. If your business is subject to state excise/franchise/sales taxes, these should be handled through your state directly. When you have a LLC, I always recommend contacting your state department to assure you've completed all business entity requirements. These are not handled through TurboTax (income tax only).