Space plane take-off & landing using only basic parts?

In the 0.24 science tree I've unlocked the Aerodynamics (tech tree tier 4), which contains the first space plane parts you can unlock.

It does not contain any landing gear. :-|

1) Can one even build a plane that takes off from a runway with these parts? 2) If so, could it land?

Yes and yes.

For takeoff, you can

• perform an all-jet VTOL
• use girders or cubic struts; if your plane has a low enough takeoff/stall speeds you can drag them with no damage
• use a very tall launch tower and rev the engine before decoupling to perform a drop takeoff
• perform a rocket-assisted forward-oriented takeoff, using the rockets to get you airborne and your jet engines to keep you that way
• turn the plane 90 degrees upward and perform a stovepipe takeoff by giving it a thrust-to-weight ratio of >= 1, or a rocket assisted takeoff
• drag your girders on radial decouplers; detach to lift off or when one breaks

For landing, you can

• use girders or struts as low-speed contacts
• use parachutes to land the plane on its belly or tail
• all of the above

The simplest way to do this is definitely a stovepipe rocket-assisted takeoff and a parachute landing. The most hardcore is the VTOL just because they're damn near impossible to build or land. (Also, VTOL protip: use action groups to switch modes between vertical engines and horizontal.)