Are the apartment fee’s refundable if not approved?

The simple answer is MAYBE. Below we outline everything to help you figure out what fees are refundable and how to get them back. 

Do homework first
“Don't apply unless you are sure” is the best policy. Once you sign the paperwork and give the landlord money, it can be difficult to negotiate or back out. There are laws that apply as explained below, but since the amounts at stake are small, the time and hassle involved in recovery make it hard to justify legal action. The best plan is to check the landlord and the property out first. See Before You Sign.

Application criteria
Landlords are now required to provide applicants with written notice of their eligibility criteria so applicants don’t pay money to be automatically denied. Remember, application fees are usually not returned even if the landlord rejects the applicant. There is one fairly recent exception -- if the landlord does not provide or post the eligibility criteria (e.g., income, criminal history), and the landlord rejects the applicant, the landlord must return everything the applicant gave them including the application fee and deposit. Section 92.3515, Property Code.

Application deposits
Landlords often refuse to hold a property without receiving a deposit. These are generally called application deposits or "hold deposits." When you give a landlord an application deposit, you are giving the landlord some assurance that you intend to sign the lease if the landlord finds you acceptable. If the landlord approves your application and you change your mind, most landlords will keep your application deposit. If a landlord rejects your application, then the landlord should return your application deposit.

Different from security deposits and application fees
Application deposits are not considered security deposits because there is no lease agreement between the parties at this point. The applicant is not a tenant so the security deposit rules do not apply. Application deposits are regulated to some extent in Subchapter I, Chapter 92 of the Texas Property Code.

An application deposit is in addition to the application fee landlords will charge you. Application fees supposedly pay for a landlord's time and trouble as well as the cost of doing a background check. Application fees are typically non-refundable (with the exception noted above).

Conversion to security deposits
Typically, if a lease is signed between the parties, then the application deposit is converted into all or part of the security deposit. Then the security deposit rules apply.

Deadline to reject and tenant and return the deposit
How long does a landlord have to either accept or reject an applicant? The law deems an applicant has been rejected after seven days from the date the person submits a complete rental application. If the landlord does not furnish the applicant with a rental application, then the applicant is deemed rejected seven days after the landlord accepts the application deposit. See Tex. Prop. Code 92.352.
The law does not put a specific deadline for the return of the deposit after an applicant has been rejected. However, many form agreements specify that a landlord has 30 days to return an application deposit after rejection.

Applicant changes mind
What happens to the deposit if the applicant changes their mind? The law is, unfortunately, not very specific. To get answers you should first look at any agreement you signed regarding the deposit. Some form agreements specifically state that if an applicant fails to sign the lease within three days after the landlord approves the applicant, the landlord can keep the entire application deposit. Even if there is no written agreement, a landlord often considers an application deposit if the applicant later decides not to lease from the landlord.
TIP: If you think you may change your mind, don't tell the landlord too soon. Remember, if the landlord rejects you first (or does not get back to you within 7 days), then the landlord has to return the entire application deposit.

Negotiate beforehand
Of course, there is always room to negotiate when you give a landlord an application deposit. Try to get a landlord to hold a place for nothing, or put in the agreement that they keep only a percentage of the deposit depending on how long they wait. (For example, if you change your mind in 24 hours they only get 25% of the deposit; after 48 hours they get 50%.)

Negotiate afterward
Some landlords recognize it is unfair to keep the entire application deposit if you change your mind in a day and they have not done much work to check you out, and have not turned other applicants away. Landlords never give back the application fee (unless required by the law mentioned above), but sometimes they will give back part of an application deposit. So, explain why you did not like the place and see if they will be decent about it and give all or part of your deposit back

Kept unfairly
If the landlord unfairly keeps your application deposit or application fee, you should at least send the landlord (the manager, management company, and/or the owner) a demand letter explaining why it is unfair and demand the return of the deposit or fee. Hopefully, you can work something out, but if you don't then consider taking the landlord to justice court (also called justice of the peace, or JP court).
If the landlord keeps your application deposit or fee in bad faith, the Texas Property Code says you are entitled to $100, three times the amount of the application deposit, and the applicant's attorney fees and court costs. Section 92.354, Property Code.

If a landlord rejects you, they must give your application deposit back promptly. If you reject the landlord you still might be entitled to some or all of your deposit back. Despite the language in an application agreement, a landlord is not entitled to keep an application deposit when the result is grossly unfair. Courts routinely hold some contractual provisions to be too harsh and will ignore them if the facts of the case are compelling.