1. There is no provision in law for the advocate to file a petition for an expeditious trial before the same trial court, however he can file a petition before high court seeking an expeditious trial. Even that may not be effective owing to various reasons, because by expeditious trial means t he cannot avoid the procedural aspects or seek them to be dispensed.
If necessary your advocate can file an advance hearing petition to hear the case in advance for the reasons stated therein, if the court is satisfied with the reasons stated therein it may allow the case to be advanced for hearing.
2. Studying LL.B cannot be claimed as a right to file petition on your own before high court, however you can file a writ petition as a party in person provided you know the procedures of law as prescribed for high court practice.
Speedy trial is a fundamental right implicit in the guarantee of life and personal liberty enshrined in Article 21 of the Constitution and any accused who is denied this right of speedy trial is entitled to approach Supreme Court under Article 32 for the purpose of enforcing such right. Hence you can file a petition before high court as a party in person too provided you have sufficient reasons to state that the proceedings are intentionally delayed or protracted.
3. If the circumstances of the cited authority suits your own case situation, and the ruling given therein applies to your situation, then you can rely upon this to your case but of course you can be able to use this only at the time of final hearing in the proposed writ petition.
4. The procedures of law has to be followed while you are pursuing a case through court.
You cannot skip the procedures for the reasons you state.
It is pertinent to implead the LRs of the deceased respondent or else your case will be dismissed for not taking proper steps to implead the LRs of the deceased respondents.
you can ask your advocate the reasons, it is not known what your advocate has done on your case, hence without knowing the proper details no opinion can be rendered on your advocate's acts, if you don't trust your advocate anymore, you are at your liberty to change your lawyer at this moment too.
You can discuss the details of your case with any lawyer of this forum by getting their contact details from this forum and opt for phone consultation so that you can get more clarity on the subject.