So I'm rewatching S3 before starting S4 and Episodes 1-4 look good. Episode 5 covers two days and I remember we settled on the first day being the Saturday before Valentine's Day which would be February 12th not the 11th as you currently have it and it ends on the next day the 13th. In Episode 6 they mention it's been over a month since Episode 5 and Sarah mentions her Geometry mid-term. High school mid-terms usually fall around March, so that on top of the over a month line both have the episode fitting sometime in March rather than late April. Jordan is seen working at the firehouse which they confirmed would be on weekends and the kids aren't in school, so I'm thinking part of the placement could be March 19th, which fits with being over a month since Episode 5, Sarah studying for a midterm, and Jonathan working at the station on a Saturday. The episode seems to cover 4 days, so I'm thinking March 18th-21st.
- Episode 7 doesn't specify how long it's been since Episode 6, but it doesn't feel that long, so I just have it as March.
- Episode 8 mentions that it's a Saturday and there's a scene before with Lois doing chemo so I have it as April 1st-2nd.
- Episode 9 has John mentions the last few days have been rough after Episode 8. Lois asks Jonathan if he's working at the firehouse that day and he says not this weekend, so I placed the episode as Saturday April 9th, fitting the few days line and the mention of Jonathan at the firehouse.
- You placed Episode 10 on a Friday. However, I feel Saturday once again works better since the kids are shown not to be at school, and with the party during the day, I feel Saturday makes sense. So, I went with April 15th, with the scene of Lois in the beginning being the 14th.
- Episode 11 picks up the night Episode 10 ends so it begins the 15th and runs through the 17th.
- Episode 12 has Lois say it's been "weeks" since Bruno's confession from Episode 11 and the reporter tells Lois it's been a couple of weeks since Sarah and Junior were saved in Episode 10. So, I kept you having the episode on a Sunday/Monday, I just pushed it back to May 1st-2nd rather than the 15th-16th. Jonathan is shown at the station. However, the kids are shown leaving school the same day so it has to be a weekday. Kyle says Jonathan's worked at the fire station for the past few months which fits with him starting after Episode 5 in February.
- Episode 13 is 32 days since Lex was released in Episode 12. This means it would go from June 3rd-4th. We see the boys' last day of their school year which fits with a Friday (3rd) in early June and the meteor shower is shown to be on a Saturday (4th). This also confirms the show's so far taken place from the beginning of the boys' freshman year (September 2020) to the end of their sophomore year (June 2022).
So, here's the changes I would make.
3x05- February 12th-13th 2022
3x06- March 18th-21st 2022
3x07- March 2022 (2005)
3x08- April 1st-2nd 2022
3x09- April 9th 2022 (2005)
3x10- April 14th-15th 2022
3x11- April 15th-17th 2022
3x12- May 1st-2nd 2022 (2005)
3x13- June 3rd-4th 2022 (May 1st-2nd 2022, May 2022).
From what I'm seeing the internal timeline of the show fits pretty well with this. The weather in Episode 13 is a little off for June, but the mention of the last day of school and summer starting is enough to overlook it. If I'm missing anything let me know, I'm not entirely sure where you got your specific dates.