Q: Does “Under Review” mean that the paper has passed the editorial check?
Status descriptions vary across journals. The submission systems of some journals use the status "under review" even when the manuscript is under the initial editorial assessment. Since the status of your paper changed to "under review" half a day after being "with editor," I'm inclined to think that "under review" in this case refers to the initial editorial screening. The editor will have to evaluate your manuscript, find reviewers, send out reviewer invitations, and acceptance emails from the reviewers before the status can change to 'under review.' Half a day seems too short a time for all these to be done. Hence, I have a feeling that your paper is possibly being reviewed by the editor currently, not by external reviewers, which unfortunately means that it still stands a chance of getting desk rejected.
Yes, "Under Review" typically indicates that the submitted paper has successfully passed the initial editorial check and has entered the peer review process. At this stage, the manuscript is being evaluated by experts in the field who will assess its quality, validity, and suitability for publication. However, it's important to note that the final decision on acceptance or rejection is made only after the completion of the peer review process. Usually, it takes 3-4 weeks to get the result.
However, Open Journal of Animal Sciences could give a feedback about 2 week, I think it is reasonable and acceptable.

