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The Orthodox practice paedocommunion and the Roman Catholics used to but don't anymore. I can't speak to your second point though.
Upvote:2
I found this website which lists currently practicing denominations:
I'm not sure which denominations/traditions have stopped practicing paedocommunion, but I would be surprised if there were any that offered communion to children of believers without also baptising them. From my understanding, the argument for paedocommunion is that the children are considered part of the covenant and are welcomed as members of the church body (this being sybolized w/ baptism), so they should be welcome as participants in all of its sacraments and not excluded from the communion table.
Upvote:2
Catholics of the Eastern Churches (Ruthenian, Ukranian, Melkite, etc), like the orthodox, baptize, commune and chrismate infants.