As mentioned in Torisuda's comment, Rachnera first appears in episode 6, but this is only right at the very end of the episode for a very short amount of time. It would be safe to say that the first 6 are spider free, the last one included so long as you turn it off right after Miia shows what she's made for dinner.
While the episodes aren't centred on one girl at each time, they all have an 'introductory episode' in which they each feature more heavily. In the case of Rachnera, this is the latter half of episode 7.
As for your other questions, I'll stick below what times she appears. The timings are taken from Crunchyroll.
Episode 6
21:18 - 21:23, 21:32 - 21:35 and 21:40 - 21:50 for a total of 18 seconds screentime. This episode should be safe to watch due to her lack of presence. The only information that you're missing out on by skipping the last few minutes is that
The man with the camera is selling Rachnera's spider webs as thread for an easy way of making money.
Episode 7
12:53 - 12:54, 13:18 - 13:25, 13:29-13:31, in which
the MON special forces team raid the house of the director. Rachnera escapes during this time.
plus 14:41 - 15:54, 15:58 - 16:24, 16:29 - 17:31, 17:38 - 18:20, 18:34 - 19:58, 20:23 - 20:33, 20:36 - 21:00, 21:04 - 21:09 and 21:13 - 22:10 for a combined total of 363 seconds of screentime.
During this time,
Rachnera first torments Kimihito a little, before explaining how she didn't get along with her host family, and ended up moving in with the director from episode 6. Smith and co. surround the building the two are in, but the situation is resolved with Rachnera moving in with Kimihito and the others.
Episode 8
1:52 - 1:55, 1:57 - 2:04, 2:08 - 2:45, 3:32 - 3:35, 4:00 - 4:19, 4:32 - 5:10, 5:25 - 5:30, 8:11 - 8:40, 8:45 - 8:52, 8:54 - 9:08, 9:24 - 9:47, 9:55 - 10:17, 10:23 - 10:27, 10:33 - 10:35 and 10:45 - 11:21 in which Rachnera
torments Kimihito, getting Cerea jealous in the process. At the end of this half, she saves Cerea and Kimihito from some thugs by tying them up.
plus 11:26 - 11:32, 12:34 - 12:46, 13:00 - 13:07, 13:30 - 14:01, 14:24 - 14:28, 15:27 - 15:34, 18:22 - 18:29, 18:38 - 18:50, 20:38 - 20:40, 20:45 - 20:47, 20:59 - 21:08 and 21:17 - 21:30 for a total of 361 seconds of screentime. In the latter half, Rachnera has no major impact on the story.
Episode 9
9:16 - 9:29, 9:32 - 10:35, 10:50 - 10:57 and 11:12 - 11:15 for a total of 86 seconds of screentime.
In which
Rachnera and Miia climb up the side of the building the Smith and Kimihito are in, only to discover that the date is a ruse to attempt to lure out the sender of a threatening letter.
There's a nice Metal Gear Solid reference as Rachnera appears for the first time in this episode, if you can stomach a bit of spider-ness.
Episode 10
14:00 - 14:08, 14:15 - 14:21, 14:37 - 14:39, 19:02 - 19:25, 19:29 - 19:40, 19:54 - 20:09, 21:26 - 21:46, for a total of 85 seconds screentime. Rachnera has no major impact on this episode.
Episode 11
13:52 - 14:06, 14:29 - 14:35, 18:28 - 18:41, 19:35 - 19:41, 20:35 - 20:46, 21:02 - 21:06, 21:22 - 21:30, 21:31 - 21:36, for a total of 67 seconds screentime. Rachnera again has no major impact on the story here. The only thing you might miss is
the explanation of the Dullahan being the writer of the second letter, and that Kimihito is "on the verge of death".
Episode 12
0:09 - 0:13, 0:30 - 0:36, 0:43 - 0:49, 06:24 - 06:28, 06:31 - 06:49, 06:54 - 06:57, 07:03 - 07:10, 07:28 - 07:35, 07:38 - 07:43, 08:01 - 08:07, 08:32 - 08:35, 08:43 - 08:48, 09:00 - 09:03 and 10:36 - 10:42
In which Rachnera
First ties up Lala the Dullahan to allow Kimihito to escape, before changing her outlook on the situation, siding with her to 'put Kimihito out of his misery without making him suffer more than he has to'. Naturally, the situation is resolved peacefully with no real harm coming to Kimihito, and the Dullahan being placed under his care.
Additionally, (notes on the Dullahan specifically)
It's revealed that Lala doesn't really see Kimihito as one marked by death, but is instead intrigued by his ability to live through the countless near death situations from the previous episodes. The first half ends ominously, with Lala stating that while Kimihito may be safe for now, Dullahans are still omens of death.
plus 12:04 - 12:12, 12:23 - 12:32, 15:01 - 15:16 and 20:24 - 20:27 for a total of 118 seconds of screentime. In the second half of this episode, Rachnera has no major impact on the story.
