Can I sue my landlord for constantly not having electricity and gas?

Failing to provide electric and gas service as incorporated in a lease is treated by the by law as a unlawful eviction for which the landlord would be liable for damages regardless of who - the landlord or the basement tenant - is turning off the switches.

You probably don't have a claim against the landlord. However, if gas and electric are to be included in your rent and by not supply them you right to quiet enjoyment is impaired, you may have a claim of constructive eviction and not have to pay rent. If this situation continues and especially if you are in a colder climate, gas for heat will become necessary. You may be well advised to start looking for a more reliable rental.

Yes. You could pursue an action for rental abatement, which would be the difference between the value of the property as warranted (e.g. with electricity and gas) and its value during any period it did not have electricity and gas. Such suits are many times brought in the small claims division.

Under Washington's Residential Landlord Tenant Act, a landlord is required to, among other things, maintain heating, electrical, plumbing and other appliances and facilities in good working order during the tenancy. Also under Washington law, a landlord impliedly warrants that the premises being rented out are/will be habitable. It is possible that not having electric and gas will justify your terminating the tenancy and potentially seeking a return of the rents you've been paying based on a breach of the Landlord's duties under the Landlord Tenant Act as well as for breaching the warranty of habitability.

The short answer is yes, assuming that the relief you wish in your suit is to be released from your lease. Generally, the threat of suit for a lease violation may be enough for your landlord to agree to release you from your lease. You may need litigation to obtain your securty deposit, if there was one. I assume by the wording of the question that no written lease exists which would specify that gas and electric are included in the rent payment. There may be issues of proof that the rent indeed was to include gas and electricity.

Yes. Not providing essential services can be grounds for terminating your lease and recovering damages in a lawsuit.