What do you call a court measure against an accused person before they are convicted or acquitted, such as releasing on bail or putting him into a remand prison? What is the umbrella term for these? In a translation of the Russian criminal procedural code, I saw the term "measure of restriction" (see p. 3 here). Is it really used in the English-speaking world?
The term is "remand" for any action where the accused is not free to move about as they please. That includes holding them in prison, releasing them on bail, or sometimes releasing them with a monitored tracking device.
the disposal of an accused person during further process of law. A person may be remanded on bail or in custody. Now includes non-secure remand, the principal example being ELECTRONIC TAGGING.
remand. (n.d.) Collins Dictionary of Law. (2006). Retrieved August 6 2020 from https://legal-dictionary.thefreedictionary.com/remand
An example of usage of the verb from Cambridge dictionary:
Of these, about 1,800 untried and more than 300 convicted unsentenced prisoners had been initially remanded into custody more than 120 days earlier.
An example of usage for the noun from Merriam-Webster:
On one side of the prison there was a block of prisoners on remand; on the other side were the convicts...
The umbrella term, which covers all possible rulings (including many not mentioned in the question) is either a bail hearing decision or just a bail decision.
From "Bail Hearing Procedures" at FindLaw (the emphasis is my own):
The following is an overview of bail hearing procedures, including the considerations of a defendant's character, whether they should be remanded, and special requirements for defendants out on bail …
Where a defendant poses a threat to the safety of the community, they may be held without bail. In other situations, federal law typically requires that a defendant in a federal criminal case be released on personal recognizance or upon execution of an unsecured appearance bond. Released defendants must not commit any crimes during the period of release.
However, if a court determines that personal recognizance or an unsecured appearance bond won't reasonably assure the defendant's appearance, or determines that the safety of a person or the community is endangered, a defendant may be released upon conditions. Federal law delineates a number of conditions that may be imposed.
Defendants may be required to:
- Limit travel (perhaps surrendering their passport);
- Maintain or seek employment;
- Undergo drug and alcohol testing;
- Undergo medical, psychiatric, or psychological treatment;
- Maintain or commence an educational program;
- Comply with a curfew;
- Refrain from excessive use of alcohol or any use of narcotic drugs;
- Remain in the custody of a designated person;
- Comply with periodic check-ins with authorities;
- Refrain from possession of a firearm;
- Refrain from contact with crime victim or others designated by the court;
- Execute a bond agreement with the court or a solvent surety in an amount as is reasonably necessary to ensure the defendant's appearance; or
- Agree to other reasonable conditions the court may impose to ensure a defendant's appearance.
Both the defendant and the government may appeal an adverse bail decision …