What are typical release cycles that are used for manga chapters or anime episodes?
I'm not asking for specific mangas/animes but simply how often on chapter/anime could be released, eg weekly or monthly.
The most typical release cycle for a manga chapter is either weekly or monthly. A lot of times the magazine will have its release schedule in the name—Weekly Shounen Jump, Monthly Shounen Magazine. Others, like Ribon or Manga Time Kirara Carat (which are both monthly) don't offer such clues.
Some magazines operate on other schedules: Hana to Yume comes out twice a month, while Dengeki Moeoh comes out every other month. Wikipedia has a list of manga magazines that give the release schedules of various magazines.
If you buy tankoubon such as the ones released outside Japan, you can usually tell which manga were weekly and which were monthly by the length of the chapters. One volume of a weekly manga contains about ten chapters. One volume of a monthly or bimonthly manga will only contain 3–5 chapters, but the chapters will be longer so the page count is about the same.
Anime pretty much are released one episode per week, every week, barring the occasional preemption by a sports game that runs late or delay due to natural disaster. You can go on the page for a simulcasting show on Crunchyroll and see the exact day and time when new episodes of a show come out. For instance, the current season's Flying Witch comes out Saturdays at 3:00 PM Pacific Time.
Anime releases are also split into cours, 13-week blocks of episodes also sometimes referred to as "seasons". (As described in What is a "cour"? and What defines one "season" of anime?.) Some shows, such as Madoka, Bakemonogatari, and Ore Imo, run one cour in length. Others, such as Kill la Kill, Fate/Zero, and Monogatari Series Second Season, run two cours, or 24–26 episodes. Still others, such as Full Metal Alchemist 2003, run four cours, or about 51 episodes. And some, like One Piece, have completely transcended the cour system and just run until the generation of viewers who were alive when it started has died off and no one remembers how Zoro and Nami joined the crew anymore.