I've applied for a UK Standard Visitor visa to attend to my sick husband, but my application was refused. How should I reapply?

You submitted a very weak application for a Standard Visitor Visa and got refused on Appendix V 4.2 (a) + (c). Usually that combination is a indicator that they decided you would go underground in the UK and eventually become reliant upon public funds. Your premise was to visit your spouse who is seriously ill. You posted your refusal notice and have some questions about it because you contemplate a fresh application.

Will an empty bank account adversely affect my application the next time despite the 3rd part sponsorship?

Yes, of course an empty bank account will hurt your chances of success. You can read in your refusal notice that they have conceded the 'bona fides' of your sponsors and have similarly conceded your sponsor's capacity. Sponsorship is not the issue and will not be the issue next time (as long as your sister-in-law extends her sponsorship offer). In this article: Should I submit bank statements when applying for a UK Visa? What do they say about me? we also explain that it's not about the ending balance. They will be looking for a cash flow stream that shows you are 'plugged in' to the local economy in the Sudan. If your bank statements are not providing that kind of picture you can expect serious problems.

Will a frank human rights claim attract more consideration from the ECO?

Let's back up and make a clarification... Human rights, in the context of Article 8, i.e., the right to family life, are not applicable to visitor applications. They apply to settlement applications only, like a spouse visa or leave to remain as a family member. Plus the courts have already ruled that visiting the UK is not a human right; to rely on Article 8, you need to make a settlement application and we don't field questions about them here (That area belongs to Expats).

So with that clarification, what is appropriate in the domain of visitor visas is compassion. ECO's have a massively broad width of discretion when compassionate circumstances appear. The discretionary consideration kicks in when they read the person's premise, it's virtually 'automatic'. And contrary to what people may think they are not heartless ogres and people who qualify get the concession all the time. It's written in your refusal notice that the ECO treated your application as compassionate. Having a compassionate occasion, however, does not always result in success.

From the ECO's Guidance...

‘Where an entry clearance application does not meet the requirements of the Immigration Rules, the Entry Clearance Officer must consider whether there are exceptional circumstances or compassionate factors which mean the Home Office should consider granting entry clearance outside the Rules.

Source ECO's Guidance.

or at least refer the case to the ECM?

Refusals where there are compassionate circumstances are automatically referred to the ECM for review (or more formally the "Referred Casework Unit"). It's standard procedure and has already happened for you.

or grant me the right to appeal in case refused?

They are not going to do that no matter what. In the upper right corner of your refusal notice you will see "GV51 Visit (NRA)", and the "NRA" stands for "No Right of Appeal". If you were close or a borderline case they would have contacted you for an interview.

In addition to my very important work, do these constitute what they consider "strong ties to home country"?

No they do not. People can collect property income from anywhere in the world, they are not a binding factor. Wedding photos are of marginal help when the other evidence is really strong, they are not fundamental enabling documents. They want to see pay slips, bank statements, employment contracts, and evidence that indicates a stable lifestyle. The stuff you listed would not carry your application.

Just to repeat, they extended credibility to your sister-in-law as a person with the capacity for sponsorship. That part of the decision-making process was decided in your favour. They treated your application as a compassionate one and your refusal was examined by the higher ups. Accordingly, making a back-to-back fresh application right away would be misconceived without correcting everything (including the required translations to English or Welsh). If you apply again, they will, however, assign it to a different ECO so as to get a fresh take on your compassionate circumstances.