The questions

1 The singer Rachel Agatha Keen performs under what mononym?
2 Which national football side has just three wins, all against Liechtenstein?
3 What religious movement was founded by Madame Blavatsky?
4 Which car-making giant was established in 1968?
5 What is the subject of Hiram Bingham’s book Lost City of the Incas?
6 Petrichor is the particular smell produced by what?
7 Which warbler is nicknamed the northern, or mock, nightingale?
8 How many sides does a hectogon have?
What links:
9 Country singer and Rhodes scholar; Mastermind’s original host; Northern Ireland secretary 1997-99?
10 Earth measurement; pebble; reunion of broken parts?
11 Financial privilege; reasonable time; Salisbury doctrine; Sewel convention?
12 Edge of Tomorrow; Groundhog Day; Run Lola Run; Source Code?
13 Dinara Safina; Jelena Janković; Karolína Plíšková; Marcelo Ríos (ranking)?
14 Armburgh; Cely; Paston; Plumpton; Stonor?
15 Cara o cruz; Kopf oder Zahl; pile ou face; krona eller klave?

The answers

1 Raye.
2 San Marino.
3 Theosophy.
4 British Leyland.
5 Machu Picchu.
6 Rain falling on (dry) soil.
7 Blackcap.
8 100.
9 First name contained within their surname: Kris Kristofferson; Magnus Magnusson; Mo Mowlam.
10 Etymologies of branches of maths: geometry (Greek); calculus (Latin); algebra (Arabic).
11 Conventions and rules observed in UK parliament.
12 Films featuring time loops.
13 Reached No 1 world tennis ranking without winning a grand slam.
14 Collections of English medieval family correspondence.
15 Heads or tails equivalent: Spanish; German; French; Swedish.