There's a scene with Shade on the landing pad if you've met her prior to picking up the Probe. It gives you certain information you can't get if you don't. Aside from reading the Wiki, anyway.
Though while not time sensitive, completing Myrellion without establishing a relationship with Shade could have dire consequences should you do Karaquest.
If you have Myrellion's Probe, and have had sex with Shade, she will leave for Uveto the next time you talk to her in the bar.
If you've done Queen Taivra's Palace, but haven't been back to your ship to pick up the Probe, Shade will have the scene (and leave for Uveto) at the landing pad, even if you didn't have sex with her.
In any case, you can get Shade to leave/not show up in Kara's 2nd quest, even if you start it after Myrellion.
Technically, you can't do the Xenogen Zil Capture quest after landing on Myrellion. The gene mods are still unlocked. You just don't get the pay and an angry mob outside the Xenogen office.
Distress Calls can be skipped without disabling them if you decline during the generic 'you're receiving a distress call' message. Once you know who it is, declining will disable that distress call/NPC. Also, declining the message involving 'floating in a nebula' and enjoying the view 5 times will disable Shizuya. If you are interested in her content, or just want to beat her up for her Custom Shock Gear, you might want to answer it.
Time Delays and things to do to be more efficient:
On Mhen'ga, I'd do Carl's quest for the ZK Rifle as a good upgrade even if you're going melee. You also probably want to visit Thare Plantation so you get the email later. You don't have to stay the night, just go through all of Prefessor Darnock's dialog. You might also want to scan the Oxonium deposit in the south Jungle for 5000 credits. The Atma Armor at the Xenogen Camp might be worth it. Airtight and Lust resistance. My Tech Specialist used it until Zheng Shi, replaced with Augment-Weave. Even better if you can get a Vanae Spear. The South Jungle is better XP anyway.
If you're a Smuggler, I'd recommend coming back to Mhen'ga at level 6+ and buying the Shock Bow or Lightning Rod from 'Crazy' Carl. The Stun Chance is really handy for a Smuggler. Also, if you're ranged, training with Tanis gets you Concussive Shot (requires a bow), which is all but guaranteed to Stun Queen Taivra at level 6 with maxed Aim, making her much easier. Lightning Rod is less critical, since Stun Chance is more common on melee weapons (read there's more than 2).
If you want to do Syri's quest, you have to have her panties. In order to get them, you have to land on Mhen'ga after becoming Syri's fuckbuddy, so you may want to do that during your first visit. Talking to her is also the easiest way to raise Intelligence without using level up points.
If you're interested in Reaha, you can only make progress on curing her addiction once per day, so getting her early might be a good idea.
On Tarkus, recruiting Anno gets you the most convenient and profitable merchant to sell to, so she's still probably worth it, even if you're rushing. Shekka has several time delays during her quest/recruitment, so starting early might also be a good idea. I always farm Sex Bots for a Hammer Shield Belt, but you could also buy a Scrap Shield from Shekka. Hammer Shield makes the Stellar Tether scenario really easy. I don't know how well the Scrap Shield performs in comparison, but 20 Shields and 25% Kinetic Resistance is a pretty big difference.
On Myrellion, the Myr Hybrid quest (producing the Gold/Red/Orange Pills) has a couple of time delays, so if you're interested, you might want to start them when you arrive. If you have an Airtight Armor (like that Atma Armor) the Nyrean Princess can't do anything to you, making getting her Reaper Armaments MK 1 Shield guaranteed.
If you're a Tech Specialist and took Attack Drone, you can upgrade Tam-Wolf to Tam-Wolf 2.0 during Kara's 2nd quest, which is pretty substantial. (Non Tech Specialist and Tech Specialist who did not take Attack Drone can repair Tam-Wolf, but it's not as critical.)
Smugglers may want to take a detour to Uveto for the Light Jetpack. +10 Evasion (actually +15 with Agility), and the ability to hit flying enemies with melee attacks.
Melee Tech Specialists and Smugglers may want to think about Shizuya's Custom Shock Gear. For a Tech Specialist, each Stun is worth +40 Shields with 50 Intelligence.
If you are using or are planning to use a Crushing melee weapon, consider returning to Shekka at level 7+ for the FZR Fire Suppression System. The Deep Freeze status effect (x2 damage with a Crushing weapon) makes it an extremely effective compliment.
You can get the password to Zheng Shi from Kiro, if you've done her distress call, or from Paige, if you've recruited her (500K credits and a week's worth of Yoga). Otherwise you have to guess or fight your way in. Or you could read the Wiki for the password, I guess. You're not winning that fight with the starter ship, so you'd have to buy a better one. Incidentally, the MS-XI is cheaper than recruiting Paige and can reliably win that fight with no modifications.
If you want to recruit Amber you have to get the Taur-centric Ship Equipment from Urbolg. According to the Wiki, you need to have met a Tauric character for the dialog option to be available. Tanis at the Mhen'ga UGC Scout Authority probably qualifies (especially if you trained with him for Concussive Shot). If you're rushing, I'm pretty sure it's possible to get to Zheng Shi without having met a Taur. You could also fight the Forgehound in Zheng Shi's Forge.