Low level definability above large cardinals

We study connections between definability in generalized descriptive set theory and large cardinals, under ZFC. We show that if $\kappa$ is a limit of measurables then there is no wellorder of a subset of $P(\kappa )$ of length $\ge {\kappa }^{+}$ which is ${\mathrm{\Sigma }}_1(V_{\kappa }\cup \mathrm{O}\mathrm{R})$, answering a question of Lücke and Müller. However, consistently, a Woodin cardinal exists and for every uncountable cardinal $\kappa$ which is not a limit of measurables, there is a ${\mathrm{\Sigma }}_1(H_{\kappa }\cup \{\kappa \})$-good wellorder of $H_{{\kappa }^{+}}$. If $\kappa$ is a limit of measurables and $\kappa$ has uncountable cofinality then there is no ${\mathrm{\Sigma }}_1(V_{\kappa }\cup \mathrm{O}\mathrm{R})$ almost disjoint family $F\subseteq P(\kappa )$ of cardinality $>\kappa$. Consistently, ${\mathrm{\Pi }}_1(\{\kappa \})$ mad families and maximal independent families $F\subseteq P(\kappa )$ exist, $\kappa$ is a limit of measurables, and more. If $\kappa$ is weakly compact and every ${\mathrm{\Sigma }}_1(V_{\kappa }\cup \{\kappa \})$ subset of $P(\kappa )$ of cardinality $>\kappa$ contains a perfect subset of the right kind, then there is an inner model with a weakly compact limit of measurables. We prove some related facts regarding ${\mathrm{\Sigma }}_1(V_{\lambda }\cup \{V_{\lambda }\}\cup \mathrm{O}\mathrm{R})$ when $I_2(\lambda )$ holds. These depend on an analysis of fixed points of linear iterations involving $I_2(\lambda )$-extenders.