Once an individual has been convicted of a crime, whether by jury or judge, the burden of proof is switched. Now the individual must prove their innocence.
It is a very difficult task to reverse a legal judgment. It does happen, but not very often. Think carefully before expending resources upon continued appeals. With each successive appeal, the burden may appear to be more difficult to prove.
Very few things that a prisoner will say are likely to have impact upon institutional policies or procedures. If your loved one has medical, mental or emotional problems before entry into prison, make sure a complete record of their healthcare needs is sent directly to the attention of the chief medical officer. Always follow up such submission with a verbal acknowledgement from the official.
Within the prison, there is a system of disciplinary procedures which can lead to various punishments for each infraction. Among these are a loss of good time (extra prison time), suspension of canteen privileges, placement in administrative segregation (the hole) without visiting privileges, denial of all contact visiting if found with contraband and possible referral for further prosecution.
If you bring any illegal items into a prison you may also be arrested and referred for felony prosecution. At a minimum you will lose your contact visiting privileges and be subject to strict inspection on any future visits.
Each state has its own parole, pardon and executive clemency policies. Review the published materials before seeking remedies through these avenues. In some jurisdictions there are procedures for petitioning for an early release based upon verified terminal illness.
There may be policies in place to request a move to a closer prison when the distance is extreme. Also be prepared to discover that your loved one may be placed in a prison far away, or even located in another state. Assignments are usually made for purposes of institutional convenience.
There is an institutional appeal policy in place to ask for review of any decision negatively impacting a prisoner during their period of incarceration. This practice must be initiated by the prisoner themselves.