Rutland councillor called for PM to be hanged.
Councillor Richard who called for Theresa May to be hanged "for treason" has admitted four criminal charges.
Other posts insulted or threatened MPs Diane Abbott and Anna Soubry.
At Birmingham Magistrates' Court, Alderman admitted sending a menacing or grossly offensive message via the public communication network.
The court heard Alderman, of Lonsdale Way, Oakham, Rutland, admitted six of a number of messages he posted were menacing or offensive. One included that the prime minister's assassination was "long overdue".
Opening the facts of the case against Alderman, prosecutor James Bruce told the court the charges related to six Facebook posts made between April and July this year.
Submitting the comments made about Ms Abbott constituted a hate crime, Mr Bruce told the court: “In essence, Mr Alderman posted publicly on Facebook when responding to news articles with comments that were a mixture of the grossly offensive and menacing.
“They relate to public figures with whom Mr Alderman disagrees with their politics, and came to the attention of the police as a result of Mr Alderman’s election to Rutland County Council on July 12.
“When members of the public looked up who their new councillor was, and looked up the postings, they decided to report them to the police.”
The court heard Alderman, of Lonsdale Way, Oakham, Rutland, admitted six of a number of messages he posted were menacing or offensive, after writing the prime minister’s assassination was “long overdue”.
A post in May used an African word for monkey to describe Ms Abbott, while a further message in June added: “The monkey is out of her tree again, send it to the animal labs.”
A further message written before Alderman’s election to the council, next to a meme criticising Nottinghamshire MP Ms Soubry, read: “Hang, shoot and drown the witch to make sure it’s dead.”
Alderman, who was reported to the police after another councillor took screenshots of the messages, was granted unconditional bail until sentencing next Thursday.
Ordering pre-sentence reports, District Judge David Robinson told Alderman: “You have pleaded guilty to these four charges and you will receive credit for that in due course.
“I am going to order the probation service to prepare pre-sentence reports to tell me more about you and the circumstances behind these offences.”
Rutland County Council said in a statement: “Councillor Alderman has admitted his wrongdoing and pleaded guilty to all four charges brought against him.
“Criminal conduct of this kind is totally unacceptable.
“Following sentencing, Councillor Alderman’s actions will be the subject of a further investigation by our own Standards Committee and reviewed against the Council’s Code of Conduct.”
Detective Constable Damian Young, of Leicestershire Police, said: “The content of the comments published by Alderman were deemed offensive.
“He is a prominent member of the Rutland community and should have known better as an elected councillor.
“We treat all reports of this nature seriously, irrespective of who has made them, and we’re pleased that he has admitted the offences.”
He was granted unconditional bail until sentencing on 4 October.
Rutland County Council said his actions were "totally unacceptable" and will be the subject of a further investigation by the authority's standards committee.
The independent councillor, described in court as "pro-Brexit and anti-immigration", refused to say whether he would resign from the council as he left the hearing.
Richard Alderman claimed during the election he was independent, whilst a local group against Rutland County Council, claimed he was there candidate via their website.
His election leaflets included the logo of the group Democracy Rutland
http://martinbrookes.blogspot.com/2018/07/richard-j-alderman-rutland-county.html
Speaking recently to a group member I was shocked to hear the person say Richard Alderman
"is only saying what we are all thinking". I would like to think that this group are minority and
the racists and bigots are not making up the majority of Rutlander's
