The common idiom is on dirait que (TLF: I.B.1.a.γ). It is followed by a verb in the indicative mood.
On dirait qu'il y a moins de sièges¹ ici que dans le métro actuel. Y a-t-il effectivement moins de sièges ?
Other impersonal constructions are possible. Avoiding the impersonal on makes for slightly more formal writing. Another common idiom is il semblerait que, followed by the subjunctive.
Il semblerait qu'il y ait ici moins de places assises que dans le métro actuel. Est-ce effectivement le cas ?
Variants include il semble que (a bit stronger than il semblerait, as the use of the conditional mood gives less weight to the semblance), and il apparaît que (rather strong: you do not expect contradiction, and rather formal: you wouldn't use it in everyday conversation, but it's what you would write in a formal report).
Like in English, personal formulations are also possible. Here are two possible translations with a construction similar to “this metro seems to have fewer seats than the current one”. The first is more formal than the second.
Ce métro semble disposer de moins de sièges que les rames actuelles.
Ce métro a l'air d'avoir moins de sièges que le métro actuel.
Your other examples would use similar phrasings.
It appears as though you haven't slept in days! Are you all right?
On dirait tu n'as pas dormi depuis des jours ! Ça va bien ?
Tu as l'air de ne pas avoir dormi depuis plusieurs jours ! Tu n'es pas bien ?
It looks like all the bathrooms here are occupied. We can go to the bar across the street.
On dirait que les toilettes sont toutes occupées. Nous pouvons aller au bar en face.
It looks like they finally launched the French Language Stack Exchange site.
On dirait que le site Stack Exchange sur la langue française a démarré.
Apparemment, le site Stack Exchange sur le français a démarré.
(Apparemment is a bit stronger, it indicates that you do not expect a refutation.)
In English, you can denote a specific method of perception through a verb. This is often not possible in French: if the method of perception is important, it will usually be conveyed through a complement or a different phrasing.
Your voice sounds strained. Have you been crying?
Tu as l'air enroué. Tu as pleuré ?
This tastes like cinnamon.
On dirait de la cannelle.
Ça a un goût de cannelle.
Something smells rotten. (figuratively: there's trouble brewing)
Ça sent le roussi.
If the reason why you think something is true is that you've been told, rather than your observation, you can use the verb paraître in the impersonal form.
I heard from someone that the next metro will have fewer seats.
Il paraît que le prochain métro aura moins de sièges.
¹ ou : de places assises