Can I be served legal papers by email?

Whether right or wrong, Texas has gone to an e-filing system which permits very important documents, including discovery requests like interrogatories, to be served via email.  This is permitted by statute.  Many have expressed concerns over the dangers of such service methods because they can easily end up in a spam folder and with no additional notice to the intended recipient.  Regardless of these concerns and protests... the method is still permitted and authorized by statute.
Interrogatories are supposed to be answered within 30 days of services, as is the case with most documents.  Responses are sent back to the other side... they are not filed with the court.   If you are getting sucked into the discovery battle, you really need to line up an attorney to represent you.  This is not a fun process... but an attorney can really help you get these answers in proper form and served on the opposing counsel.
You will not automatically lose your case if you fail to answer, but it could hinder your case if you don't properly answer the discovery requests.  If your computer is down, go to a public library, access your emails, and print off any documents so that you can respond to them.
As far as getting help... many law schools do offer clinics and pro-bono clinics... so this is a good starting point.  You should also call the district clerk and inquire about any other programs, pro bono clinics, or legal aid groups in your area.  Also reach out to the local bar association to get the dates for any legal clinics sponsored by the local bar association.  Even if they don't formally represent you, they can provide you valuable guidance in responding to discovery requests and service of your own requests on your husband.