The apps i'm going to propose are available through F-Droid. The name F-Droid refers to both A.) a repository for open source android apps and to B.) an android app used to browse, download, install an manage those apps on your android device.
You might want to check out this tutorial for information on how to install F-Droid or apk-files downloaded from F-Droid.
If you don't want to use F-Droid or sideload apps on your device, maybe you can find some of these apps in the Play Store as well.
The Contacts app in android normally has a feature to import or export the contacts to a text file (.vcf). If it doesn't you can install this open source contacts app that can definitely do it:
This depends on how you store your calendar events. In Android, it is common to store the events in a certain calendar, usually tied to an E-Mail account, this can also be your google account. In these cases, the calendar events are stored online with your E-Mail provider and should be accesible from any device with that Mail account properly set up for calendar syncing. If there is a website where you can log in and check your mail, chances are there is a calendar function on that site as well. If you can log into your Mail account using a normal browser and find your calendar events there, they are already backed up to the server of your Mail Provider.
If you want a local backup of these Events or keep them stored in a local calendar on your device, https://f-droid.org/app/org.sufficientlysecure.ical can export and import your calendar events to and from .ics files.
Note that the Android Calendar backend might discard passed events, in which case they cannot be exported using this method.
If your events are stored in your E-Mail account, chances are that these passed events that are no longer displayed/exportable on your Android device are still available online and stay stored on the server of your E-Mail provider - Android usually just stops syncing these events and removes them from your calendar view.
For the default preinstalled browser in android it is also possible to back up and restore bookmarks. From F-Droid https://f-droid.org/app/de.shandschuh.slightbackup can do it.
Though, it should be mentioned that this app hasn't been updated a long time and might thus not work too well with modern versions of android. Since i don't use the bookmark feature i can't attest how good it works but giving it a try shouldn't hurt either - as long as you don't try to restore data before testing that nothing gets deleted or overwritten on the device where you want to restore you shouldn't lose any data by trying.
As you stated that you are using a samsung phone the browser will likely be custom made by samsung, so your best bet would probably be finding an export function built into the browser.
If the same circumstances described here apply to your browser app, your chances don't look very good.